Repozytorim Annales UMCS Sectio A - Matematyka:
Liczba artykułów w bazie: 228 Format SWF: 192 Format DJVU: 9 Format PDF: 228 Razem plików: 429

Volume 69 - 2015

Article 000PL: Spis treści
EN: Table of contents
-

- Full text in PDF format

Article 01EN: Components with the expected codimension in the moduli scheme of stable spin curves
1-4

EDOARDO BALLICO


Department of Mathematics, University of Trento, 38123 Povo (TN) Italy e-mail: ballico@science.unitn.it

Here we study the Brill–Noether theory of “extremal” Cornalba’s theta-characteristics on stable curves C of genus g, where “extremal” means that they are line bundles on a quasi-stable model of C with ](Sing(C)) exceptional components.
  1. Arbarello, E., Cornalba, M., Griffiths, P. A., Geometry of Algebraic Curves. Vol. II, Springer, Berlin, 2011.
  2. Ballico, E., Sections of theta-characteristics on stable curves, Int. J. Pure Appl. Math. 54, No. 3 (2009), 335–340.
  3. Benzo, L., Components of moduli spaces of spin curves with the expected codimension, Mathematische Annalen (2015), DOI 10.1007/s00208-015-1171-6, arXiv:1307.6954.
  4. Caporaso, L., A compactification of the universal Picard variety over the moduli space of stable curves, J. Amer. Math. Soc. 7, No. 3 (1994), 589–660.
  5. Cornalba, M., Moduli of curves and theta-characteristics. Lectures on Riemann surfaces (Trieste, 1987), World Sci. Publ., Teaneck, NJ, 1989, 560–589.
  6. Farkas, G., Gaussian maps, Gieseker–Petri loci and large theta-characteristics, J. Reine Angew. Math. 581 (2005), 151–173.
  7. Fontanari, C., On the geometry of moduli of curves and line bundles, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16, No. 1 (2005), 45–59.
  8. Harris, J., Theta-characteristics on algebraic curves, Trans. Amer. Math. Soc. 271 (1982), 611–638.
  9. Jarvis, T. J., Torsion-free sheaves and moduli of generalized spin curves, Compositio Math. 110, No. 3 (1998), 291–333.
10.1515/umcsmath-2015-0009
- Full text in PDF format

Article 02EN: Statuses and double branch weights of quadrangular outerplanar graphs
5-21

HALINA BIELAK, KAMIL POWROZNIK


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, hbiel@hektor.umcs.lublin.pl, kamil.pawel.powroznik@gmail.com

In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.
  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Application, Macmillan London and Elsevier, New York, 1976.
  2. Entringer, R. C., Jackson, D. E., Snyder, D. A., Distance in graphs, Czech. Math. J. 26 (1976), 283–296.
  3. Jordan, C., Sur les assembblages des lignes, J. Reine Angnew. Math. 70 (1896), 185–190.
  4. Kang, A. N. C., Ault, D. A., Some properties of a centroid of a free tree, Inform. Process. Lett. 4, No. 1 (1975), 18–20.
  5. Kariv, O., Hakimi, S. L., An algorithmic approach to network location problems. II: The p-medians, SIAM J. Appl. Math. 37 (1979), 539–560.
  6. Korach, E., Rotem, D., Santoro, N., Distributed algorithms for finding centers and medians in networks, ACM Trans. on Programming Languages and Systems 6, No. 3 (1984), 380–401.
  7. Lin, Ch., Shang, J-L., Statuses and branch-weights of weighted trees, Czech. Math. J. 59 (134) (2009), 1019–1025.
  8. Lin, Ch., Tsai, W-H., Shang, J-L., Zhang, Y-J., Minimum statuses of connected graphs with fixed maximum degree and order, J. Comb. Optim. 24 (2012), 147–161.
  9. Mitchell, S. L., Another characterization of the centroid of a tree, Discrete Math. 23 (1978), 277–280.
  10. Proskurowski, A., Centers of 2-trees, Ann. Discrete Math. 9 (1980), 1–5.
  11. Slater, P. J., Medians of arbitrary graphs, J. Graph Theory 4 (1980), 289–392.
  12. Szamkołowicz, L., On problems related to characteristic vertices of graphs, Colloq. Math. 42 (1979), 367–375.
  13. Truszczynski, M., Centers and centroids of unicyclic graphs, Math. Slovaka 35 (1985), 223–228.
  14. Zelinka, B., Medians and peripherians of trees, Arch. Math. (Brno) 4, No. 2 (1968), 87–95.
10.1515/umcsmath-2015-0010
- Full text in PDF format

Article 03EN: A multidimensional singular stochastic control problem on a finite time horizon
23-57

MARCIN BORYC, ŁUKASZ KRUK


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, borycmarcin@gmail.com, lkruk@hektor.umcs.lublin.pl

A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.
  1. Budhiraja, A., Ross, K., Existence of optimal controls for singular control problems with state constraints, Ann. Appl. Probab. 16, No. 4 (2006), 2235–2255.
  2. Chow, P. L., Menaldi, J. L., Robin, M., Additive control of stochastic linear systems with finite horizon, SIAM J. Control Optim. 23, No.6 (1985), 858–899.
  3. Dufour, F., Miller, B., Singular stichastic control problems, SIAM J. Control Optim. 43, No. 2 (2004), 708–730.
  4. Evans, L. C., Partial Differential Equations, American Mathematical Society, Providence, RI, 1998.
  5. Fleming, W. H., Soner, H. M., Controlled Markov Processes and Viscosity Solutions, Springer, New York, 2006.
  6. Haussman, U. G., Suo, W., Singular optimal stochastic controls. I. Existence, SIAM J. Control Optim. 33, No. 3 (1995), 916–936.
  7. Karatzas, I., Shreve, S. E., Brownian Motion and Stochastic Calculus, Springer- Verlag, New York, 1988.
  8. Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part I: The Skorokhod problem, SIAM J. Control Optim. 38, No. 5 (2000), 1603– 1622.
  9. Kruk, Ł., Optimal policies for n-dimensional singular stochastic control problems, Part II: The radially symmetric case. Ergodic control, SIAM J. Control Optim. 39, No. 2 (2000), 635–659.
  10. Krylov, N. V., Controlled Diffusion Processes, Springer-Verlag, New York, 1980.
  11. Menaldi, J. L., Taksar, M. I., Optimal correction problem of a multidimensional stochastic system, Automatica J. IFAC 25, No. 2 (1989), 223–232.
  12. Rudin, W., Functional Analysis, McGraw-Hill Book Company, New York, 1991.
  13. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill Book Company, New York, 1976.
  14. Soner, H. M., Shreve, S. E., Regularity of the value function for a two-dimensional singular stochastic control problem, SIAM J. Control Optim. 27 (1989), 876–907.
  15. Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control, Applied stochastic analysis (London, 1989), Stochastics Monogr. 5, Gordon and Breach, New York, 1991, 265–301.
  16. Soner, H. M., Shreve, S. E., A free boundary problem related to singular stochastic control: the parabolic case, Comm. Partial Differential Equations 16 (1991), 373–424.
  17. S. A. Williams, P. L. Chow and J. L. Menaldi, Regularity of the free boundary in singular stochastic control, J. Differential Equations 111 (1994), 175–201.
  18. http://en.wikipedia.org/wiki/Gronwall’s inequality, 24.09.2013.
10.1515/umcsmath-2015-0011
- Full text in PDF format

Article 04EN: On pseudo-BCI-algebras
59-71

GRZEGORZ DYMEK


Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland, e-mail: gdymek@o2.pl

The notion of normal pseudo-BCI-algebras is studied and some characterizations of it are given. Extensions of pseudo-BCI-algebras are also considered.
  1. Dudek, W. A., Jun, Y. B., Pseudo-BCI algebras, East Asian Math. J. 24 (2008), 187–190.
  2. Dymek, G., Atoms and ideals of pseudo-BCI-algebras, Comment. Math. 52 (2012),
  3. Dymek, G., p-semisimple pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 19 (2012), 461–474.
  4. Dymek, G., On compatible deductive systems of pseudo-BCI-algebras, J. Mult.-Valued Logic Soft Comput. 22 (2014), 167–187.
  5. Dymek, G., Kozanecka-Dymek, A., Pseudo-BCI-logic, Bull. Sect. Logic Univ. Łódz 42 (2013), 33–42.
  6. Halaˇs, R., K¨uhr, J., Deductive systems and annihilators of pseudo-BCK-algebras, Ital. J. Pure Appl. Math. 25 (2009).
  7. Iorgulescu, A., Algebras of Logic as BCK Algebras, Editura ASE, Bucharest, 2008.
  8. Is´eki, K., An algebra related with a propositional calculus, Proc. Japan Acad. 42 (1966), 26–29.
  9. Jun, Y. B., Kim, H. S., Neggers, J., On pseudo-BCI ideals of pseudo BCI-algebras, Mat. Vesnik 58 (2006), 39–46.
10.1515/umcsmath-2015-0012
- Full text in PDF format

Article 05EN: Pattern avoidance in partial words over a ternary alphabet
73-82

ADAM GĄGOL


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: adam.gagol@gmail.com

Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with m distinct variables and of length at least 2m is avoidable over a ternary alphabet and if the length is at least 3*2m-1 it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words.
  1. Blanchet-Sadri, F., Woodhouse, B., Strict Bounds for Pattern Avoidance, Theoret. Comput. Sci. 506 (2013), 17–28.
  2. Cassaigne, J., Motifs ´evitables et r´egularit´es dans les mots, PhD Thesis, Universit´e Paris VI, July 1994.
  3. Flajolet, P., Sedgewick, R., Analytic Combinatorics. Cambridge University Press, 2009, ISBN 978-0-521-89806-5, electronic version.
  4. Grytczuk, J., Kozik, J., Micek, P., A new approach to nonrepetitive sequences, Random Structures Algorithms 42 (2013), 214–225.
  5. Krieger, D., Ochem, P., Rampersad, N., Shallit, J., Avoiding Approximate Squares, Lecture Notes in Computer Science, Vol. 4588, 2007, 278–289.
  6. Lothaire, M., Algebraic Combinatorics on Words, Cambridge University Press, Cambridge, 2002.
  7. Moser, R. A., Tardos, G., A constructive proof of the general lovasz local lemma, J. ACM 57 (2) (2010), Art. 11, 15 pp.
  8. Ochem, P., Pinlou, A., Application of entropy compression in pattern avoidance, Electron. J. Combin. 21, P2.7 (2014).
  9. Zydron, A., Unikalnosc bezjednostkowych wzorców o duzej liczbie zmiennych, MsC Thesis, Jagiellonian University, 2013.
10.1515/umcsmath-2015-0013
- Full text in PDF format

Article 06EN: Proximinality and co-proximinality in metric linear spaces
83-90

NARANG T. D. 1,SAHIL GUPTA 2


Department of Mathematics, Guru Nanak Dev University, Amritsar-143005 Amritsar-143005, India,e-mail: tdnarang1948@yahoo.co.in e-mail: sahilmath@yahoo.in

As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces.
  1. Cheney, E. W., Introduction to Approximation Theory, McGraw Hill, New York, 1966.
  2. Franchetti, C., Furi, M., Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 1045–1048.
  3. Mazaheri, H., Maalek Ghaini, F. M., Quasi-orthogonality of the best approximant sets, Nonlinear Anal. 65 (2006), 534–537.
  4. Mazaheri, H., Modaress, S. M. S., Some results concerning proximinality and coproximinality, Nonlinear Anal. 62 (2005), 1123–1126.
  5. Muthukumar, S., A note on best and best simultaneous approximation, Indian J. Pure Appl. Math. 11 (1980), 715–719.
  6. Narang, T. D., Best approximation in metric spaces, Publ. Sec. Mat. Univ. Autonoma Barcelona 27 (1983), 71–80.
  7. Narang, T. D., Best approximation in metric linear spaces, Math. Today 5 (1987), 21–28.
  8. Narang, T. D., Singh, S. P., Best coapproximation in metric linear spaces, Tamkang J. Math. 30 (1999), 241–252.
  9. Papini, P. L., Singer, I., Best coapproximation in normed linear spaces, Monatsh. Math. 88 (1979), 27–44.
  10. Rao, K. Chandrasekhara, Functional Analysis, Narosa Publishing House, New Delhi, 2002.
  11. Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Springer-Verlag, New York, 1970.
10.1515/umcsmath-2015-0014
- Full text in PDF format

Article 07EN: The natural transformations between r-th order prolongation of tangent and cotangent bundles over Riemannian manifolds
91-108

MARIUSZ PLASZCZYK


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: mariusz.piotr.plaszczyk@gmail.com

If (M; g) is a Riemannian manifold then there is the well-known base preserving vector bundle isomorphism TM ! TM given by v 7! g(v;
  1. Epstein, D. B. A., Natural tensors on Riemannian manifolds, J. Differential Geom. 10 (1975), 631–645.
  2. Kobayashi, S., Nomizu, K., Foundations of Differential Geometry, Vol. I, J. Wiley- Interscience, New York–London, 1963.
  3. Kol´aˇr, I., Connections on higher order frame bundles and their gauge analogies, Variations, Geometry and Physics, Nova Sci. Publ., New York, 2009, 167–188.
  4. Kol´aˇr, I., Michor, P. W., Slov´ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
  5. Kurek, J., Mikulski, W. M., The natural transformations between r-tangent and rcotangent bundles over Riemannian manifolds, Ann. Univ. Mariae Curie-Skłodowska Sect. A 68 (2) (2014), 59–64.
  6. Kurek, J., Mikulski, W. M., The natural operators lifting connections to tensor powers of the cotangent bundle, Miskolc Mathematical Notes 14, No. 2 (2013), 517–524.
  7. Mikulski, W. M., Lifting connections to the r-jet prolongation of the cotangent bundle, Math. Appl. (Brno) 3 (2014), 115–124.
10.1515/umcsmath-2015-0015
- Full text in PDF format

Article 08EN: A-manifolds on a principal torus bundle over an almost Hodge A-manifold base
109-119

GRZEGORZ ZBOROWSKI


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: zzzbor@gmail.com

An A-manifold is a manifold whose Ricci tensor is cyclic-parallel, equivalently it satisfies rX Ric(X;X) = 0. This condition generalizes the Einstein condition. We construct new examples of A-manifolds on r-torus bundles over a base which is a product of almost Hodge A-manifolds.
  1. Besse, A., Einstein Manifolds, Springer-Verlag, Berlin, Heidelberg, 1987.
  2. Gray, A., Einstein-like manifolds which are not Einstein, Geom. Dedicata 7 (1978), 259–280.
  3. Jelonek, W., On A-tensors in Riemannian geometry, preprint PAN 551, 1995.
  4. Jelonek, W., K-contact A-manifolds, Colloq. Math. 75 (1) (1998), 97–103.
  5. Jelonek, W., Almost K¨ahler A-structures on twistor bundles, Ann. Glob. Anal. Geom. 17 (1999), 329–339.
  6. Kobayashi, S., Principal fibre bundles with the 1-dimensional toroidal group, Tohoku Math. J. 8 (1956), 29–45.
  7. Moroianu, A., Semmelmann, U., Twistor forms on K¨ahler manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003), 823–845.
  8. O’Neill, B., The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469.
  9. Pedersen, H., Todd, P., The Ledger curvature conditions and D’Atri geometry, Differential Geom. Appl. 11 (1999), 155–162.
  10. Sekigawa, K., Vanhecke, L., Symplectic geodesic symmetries on K¨ahler manifolds, Quart. J. Math. Oxford Ser. (2) 37 (1986), 95–103.
  11. Semmelmann, U., Conformal Killing forms on Riemannian manifolds, preprint, arXiv:math/0206117.
  12. Tang, Z., Yan, W., Isoparametric foliation and a problem of Besse on generalizations of Einstein condition, preprint, arXiv:math/1307.3807.
  13. Wang, M. Y., Ziller, W., Einstein metrics on torus bundles, J. Differential Geom. 31 (1990), 215–248.
  14. Zborowski, G., Construction of an A-manifold on a principal torus bundle, Ann. Univ. Paedagog. Crac. Stud. Math. 12 (2013), 5–19.
10.1515/umcsmath-2015-0016
- Full text in PDF format

Volume 68 - 2014

Article 00PL: Spis treści
EN: Table of contents
-

- Full text in PDF format

Article 01EN: The Fekete–Szeg¨o problem for a class of analytic functions defined by Carlson–Shaffer operator
1-10

OM P. AHUJA 1, HALIT ORHAN 2


1 Department of Mathematical Sciences, Kent State University, Burton Ohio 44021-9500 U.S.A., e-mail: oahuja@kent.edu
2 Department of Mathematics Faculty of Science, Ataturk University Erzurum, 25240 Turkey, e-mail: orhanhalit607@gmail.com

In the present investigation we solve Fekete–Szeg¨o problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.
  1. Abdel-Gawad, H. R., Thomas, D. K., Fekete–Szeg¨o problem for strongly close-toconvex function, Proc. Amer. Math. Soc. 114 (2) (1992), 345–349.
  2. Al-Oboudi, F. M., On univalent functions defined by a generalized S˘al˘agean operator, Int. J. Math. Math. Sci., no. 25–28 (2004), 1429–1436.
  3. Brannan D. A., Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. 2 (1) (1969), 431–443.
  4. Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737–745.
  5. C¸ a˘glar, M., Deniz, E., Orhan, H., Coefficient bounds for a subclass of starlike functions of complex order, Appl. Math. Comput. 218 (2011), 693–698.
  6. Darus, M., Akbarally, A., Coefficient estimates for Ruscheweyh derivatives, Int. J. Math. Math. Sci. 36 (2004), 1937–1942.
  7. Deniz, E., Orhan, H., The Fekete–Szeg¨o problem for a generalized subclass of analytic functions, Kyungpook Math. J. 50 (2010), 37–47.
  8. Deniz, E., C¸ a˘glar, M., Orhan, H., The Fekete–Szeg¨o problem for a class of analytic functions defined by Dziok–Srivastava operator, Kodai Math. J. 35 (2012), 439–462.
  9. Dziok, J., Classes of functions defined by certain differential-integral operators, J. Comput. Appl. Math. 105 (1999), 245–255.
  10. Fekete, M., Szeg¨o, G., Eine Bermerkung uber ungerade schlichte funktionen, J. London Math. Soc. 8 (1933), 85–89.
  11. Frasin, B., Darus, M., On Fekete–Szeg¨o problem using Hadamard product, Int. J. Math. Math. Sci. 12 (2003), 1289–1295.
  12. Goel, R. M., Mehrok, B. S., A coefficient inequality for certain classes of analytic functions, Tamkang J. Math. 22 (2) (1995), 153–163.
  13. Koeghe, F. R., Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12.
  14. Lashin, A. Y., Starlike and convex functions of complex order involving a certain linear operator, Indian J. Pure Appl. Math. 34 (7) (2003), 1101–1108.
  15. Orhan, H., Kamali, M., On the Fekete–Szeg¨o problem, Appl. Math. Comput. 144 (2003), 181–186.
  16. Orhan, H., Raducanu, D., Fekete–Szeg¨o problem for strongly starlike functions associated with generalized hypergeometric functions, Math. Comput. Modelling 50 (2009), 430–438.
  17. Orhan, H., Ya˘gmur, N., Deniz, E., Coefficient inequality for a generalized subclass of analytic functions, Bull. Transilv. Univ. Bra¸sov Ser. III 4(53), no. 1 (2011), 51–57.
  18. Orhan, H., Deniz, E., C¸ a˘glar, M., Fekete–Szeg¨o problem for certain subclasses of analytic functions, Demonstratio Math. 45, no. 4 (2012), 835–846.
  19. Pommerenke, Ch., Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.
  20. R˘aducanu, D., Orhan, H., Subclasses of analytic functions defined by a generalized differential operator, Int. J. Math. Anal. (Ruse) 4 (1) (2010), 1–15.
  21. Ravichandran, V., Kumar, S. S., On a class of analytic functions involving Carlson– Shaffer linear operator, Riv. Math. Univ. Parma 7 (3) (2004), 35–48.
  22. Ruscheweyh, S., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
  23. S˘al˘agean, G. S., Subclasses of univalent functions, Complex analysis – fifth Romanian–Finnish seminar, Part 1 (Bucharest, 1981), Lecture Notes in Math. 1013, Springer, Berlin, 1983, 362–372.
  24. Srivastava, H. M., Owa, S. (Eds.), Current Topics in Analytic Fuction Theory, World Scientific Publishing, New Jersey, 1992.
  25. Srivastava, H. M., Mishra, A. K., Das, M. K., The Fekete–Szeg¨o problem for a subclass of close-to-convex functions, Complex Variable Theory Appl. 44 (2) (2001), 145–163.
10.2478/umcsmath-2014-0001
- Full text in PDF format

Article 02EN: On the birational gonalities of smooth curves
11-20

E. BALLICO


Dept. of Mathematics University of Trentov, Italy, e-mail: ballico@science.unitn.it

Let C be a smooth curve of genus g. For each positive integer r the birational r-gonality sr(C) of C is the minimal integer t such that there is L Pict (C) with h0(C;L) = r + 1. Fix an integer r >= 3. In this paper we prove the existence of an integer gr such that for every integer g >= gr there is a smooth curve C of genus g with sr+1(C)=(r + 1) > sr(C)=r, i.e. in the sequence of all birational gonalities of C at least one of the slope inequalities fails.
  1. Coppens, M., Martens, G., Linear series on 4-gonal curves, Math. Nachr. 213, no. 1 (2000), 35–55.
  2. Eisenbud, D., Harris, J., On varieties of minimal degree (a centennial account), Algebraic Geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), 3–13, Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987.
  3. Harris, J., Eisenbud, D., Curves in projective space, S´eminaire de Math´ematiques Sup´erieures, 85, Presses de l’Universit´e de Montr´eal, Montr´eal, Que., 1982.
  4. Hatshorne, R., Algebraic Geometry, Springer-Verlag, Berlin, 1977.
  5. Laface, A., On linear systems of curves on rational scrolls, Geom. Dedicata 90, no. 1 (2002), 127–144; generalized version in arXiv:math/0205271v2.
  6. Lange, H., Martens, G., On the gonality sequence of an algebraic curve, Manuscripta Math. 137 (2012), 457–473.
10.2478/umcsmath-2014-0002
- Full text in PDF format

Article 03EN: The Turan number of the graph 3P4
21-29

HALINA BIELAK 1, SEBASTIAN KIELISZEK 2


1 Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: hbiel@hektor.umcs.lublin.pl
2 Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: sebastian.lukasz.kieliszek@gmail.com

Let ex(n,G) denote the maximum number of edges in a graph on n vertices which does not contain G as a subgraph. Let Pi denote a path consisting of i vertices and let mPi denote m disjoint copies of Pi. In this paper we count ex(n,3P4).
  1. Bushaw, N., Kettle, N., Tur´an numbers of multiple paths and equibipartite forests, Combin. Probab. Comput. 20 (2011), 837–853.
  2. Erd˝os, P., Gallai, T., On maximal paths and circuits of graphs, Acta Math. Acad. Sci. Hungar. 10 (1959), 337–356.
  3. Faudree, R. J., Schelp, R. H., Path Ramsey numbers in multicolorings, J. Combin. Theory Ser. B 19 (1975), 150–160.
  4. Gorgol, I., Tur´an numbers for disjoint copies of graphs, Graphs Combin. 27 (2011), 661–667.
  5. Harary, F., Graph Theory, Addison-Wesley, Mass.-Menlo Park, Calif.–London, 1969.
10.2478/umcsmath-2014-0003
- Full text in PDF format

Article 04EN: Properties of the determinant of a rectangular matrix
31-41

ANNA MAKAREWICZ 1, PIOTR PIKUTA2, DOMINIK SZAŁKOWSKI3


1 Lublin University of Technology, Department of Applied Mathematics, ul. Nadbystrzycka 38 D, 20-618 Lublin, Poland, e-mail: anna makarewicz@o2.pl
2 Institute of Mathematics Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin Poland, e-mail: ppikuta@poczta.umcs.lublin.pl
3 Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: dominik.szalkowski@umcs.lublin.pl

In this paper we present new identities for the Radic’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column.
  1. Amiri, M., Fathy, M., Bayat, M., Generalization of some determinantal identities for non-square matrices based on Radic’s definition, TWMS J. Pure Appl. Math. 1, no. 2 (2010), 163–175.
  2. Radic, M., A definition of determinant of rectangular matrix, Glas. Mat. Ser. III 1(21) (1966), 17–22.
  3. Radic, M., About a determinant of rectangular 2  n matrix and its geometric interpretation, Beitr¨age Algebra Geom. 46, no. 2 (2005), 321–349.
  4. Radic, M., Areas of certain polygons in connection with determinants of rectangular matrices, Beitr¨age Algebra Geom. 49, no. 1 (2008), 71–96.
  5. Radic, M., Certain equalities and inequalities concerning polygons in R2, Beitr¨age Algebra Geom. 50, no. 1 (2009), 235–248.
  6. Radic, M., Suˇsanj, R., Geometrical meaning of one generalization of the determinant of a square matrix, Glas. Mat. Ser. III 29(49), no. 2 (1994), 217–233.
10.2478/umcsmath-2014-0004
- Full text in PDF format

Article 05EN: A fixed point theorem for nonexpansive compact self-mapping
43-47

T. D. NARANG


Department of Mathematics Guru, Nanak Dev University, Amritsar -143005, India, e-mail: tdnarang1948@yahoo.co.in

A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.
  1. Agarwal, R. P., Meehan, M., O’Regan, D., Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001.
  2. Beg, I., Abbas, M., Fixed points and best approximation in Menger convex metric spaces, Arch. Math. (Brno) 41 (2005), 389–397.
  3. Beg, I., Shahzad, N., Iqbal, M., Fixed point theorems and best approximation in convex metric spaces, J. Approx. Theory 8 (1992), 97–105.
  4. Dotson Jr., W. G., Fixed-point theorems for nonexpansive mappings on starshaped subset of Banach spaces, J. London Math. Soc. 2 (1972), 408–410.
  5. Dotson Jr., W. G., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155–156.
  6. Dugundji, J., Granas, A., Fixed Point Theory, PWN-Polish Sci. Publ., Warszawa, 1982.
  7. Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990.
  8. Guay, M. D., Singh, K.L., Whitfield, J. H. M., Fixed point theorems for nonexpansive mappings in convex metric spaces, Proc. Conference on nonlinear analysis (Ed. S.P. Singh and J.H. Bury), Marcel Dekker, New York, 1982, 179–189.
  9. Habiniak, L., Fixed point theory and invariant approximations, J. Approx. Theory 56 (1989), 241–244.
  10. Singh, S., Watson, B., Srivastava, P., Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic Publishers, Dordrecht, 1997.
  11. Schauder, J., Der fixpunktsatz in funktionaraumen, Studia Math. 2 (1930), 171–180.
  12. Takahashi, W., A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep. 22 (1970), 142–149.
10.2478/umcsmath-2014-0005
- Full text in PDF format

Article 06EN: Weighted sub-Bergman Hilbert spaces
49-57

MARIA NOWAK 1, RENATA ROSOSZCZUK 2


1 Instytut Matematyki UMCS, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin Poland, e-mail: mt.nowak@poczta.umcs.lublin.pl
2 Politechnika Lubelska, Katedra Matematyki Stosowanej, ul. Nadbystrzycka 38, 20-618 Lublin, Poland, e-mail: renata.rososzczuk@gmail.com

We consider Hilbert spaces which are counterparts of the de Branges–Rovnyak spaces in the context of the weighted Bergman spaces A2a, -1 < a < . These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers.
  1. Abkar, A., Jafarzadeh, B., Weighted sub-Bergman Hilbert spaces in the unit disk, Czechoslovak Math. J. 60 (2010), 435–443.
  2. Cowen, C., MacCluer, B., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.
  3. Hedenmalm, H., Korenblum, B., Zhu, K., Theory of Bergman Spaces, Spinger-Verlag, New York, 2000.
  4. Sarason, D., Sub-Hardy Hilbert Spaces in the Unit Disk, Wiley, New York, 1994.
  5. Sultanic, S., Sub-Bergman Hilbert spaces, J. Math. Anal. Appl. 324 (2006), 639–649.
  6. Symesak, F., Sub-Bergman spaces in the unit ball of Cn, Proc. Amer. Math. Soc. 138 (2010), 4405–4411.
  7. Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, Indiana Univ. Math. J. 45 (1996), 165–176.
  8. Zhu, K., Sub-Bergman Hilbert spaces in the unit disk, II, J. Funct. Anal. 202 (2003), 327–341.
  9. Zhu, K., Operator Theory in Function Spaces, Dekker, New York, 1990.
  10. Zorboska, N., Composition operators induced by functons with supremum strictly smaller than 1, Proc. Amer. Math. Soc. 106 (1989), 679–684.
10.2478/umcsmath-2014-0006
- Full text in PDF format

Article 07EN: On a subordination result for analytic functions defined by convolution
59-66

E. A. OYEKAN 1, T. O. OPOOLA 2


1 Department of Mathematics and Statistics, Bowen University, Iwo, Osun State, Nigeria, e-mail: shalomfa@yahoo.com
1 Department of Mathematics, University of Ilorin, Ilorin, Nigeria, e-mail: opoolato@unilorin.edu.ng

In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U.
  1. Aouf, M. K., Shamandy, A., Mostafa, A. O., El-Emam, F., Subordination results associated with -uniformly convex and starlike functions, Proc. Pakistan Acad. Sci. 46, no. 2 (2009), 97–101.
  2. Attiya, A. A., Cho, N. E., Kutbi, M. A., Subordination properties for certain analytic functions, Int. J. Math. Math. Sci. 2008, Article ID 63825 (2008).
  3. Latha, S., Shivarudrappa, L., A note on coefficient estimates for a class of analytic functions, Advances in Inequalities for Series (2008), 143–149.
  4. Selvaraj, C., Karthikeyan, K. R., Certain subordination results for a class of analytic functions defined by the generalized integral operator, Int. J. Comput. Math. Sci. 2, no. 4 (2008), 166–169.
  5. Wilf, H. S., Subordinating factor sequences for some convex maps of unit circle, Proc. Amer. Math. Soc. 12 (1961), 689–693.
10.2478/umcsmath-2014-0007
- Full text in PDF format

Article 08EN: The constructions of general connections on second jet prolongation
67-89

MARIUSZ PLASZCZYK


Institute of Mathematics, Maria Curie-Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland, e-mail: mariusz.piotr.plaszczyk@gmail.com

We determine all natural operators D transforming general connections
  1. Doupovec, M., Mikulski, W., Holonomic extension of connections and symmetrization of jets, Rep. Math. Phys. 60 (2007), 299–316.
  2. Ehresmann, C., Sur les connexions d’ordre sup´erieur, Atti del V. Cong. del’Unione Mat. Italiana, 1955, Cremonese, Roma, 1956, 344–346.
  3. Kol´aˇr, I., Higher order absolute differentiation with respect to generalized connections, Differential Geometry, Banach Center Publ. 12, PWN-Polish Sci. Publ., Warszawa, 1984, 153–162.
  4. Kol´aˇr, I., Michor, P. W., Slov´ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
  5. Kol´aˇr, I., Prolongations of generalized connections, Differential Geometry (Budapest, 1979), Colloq. Math. Soc. J´anos Bolyai, 31, North-Holland, Amsterdam, 1982, 317– 325.
  6. Kol´aˇr, I., On the torsion free connections on higher order frame bundles, New Developments in Differential Geometry (Debrecen, 1994), Proceedings (Conference in Debrecen), Math. Appl., 350, Kluwer Acad. Publ., Dordrecht, 1996, 233–241.
  7. Kurek, J., Mikulski, W., On prolongations of projectable connections, Ann. Polon. Math. 101 (2011), no. 3, 237–250.
  8. Mikulski, W., On “special” fibred coordinates for general and classical connections, Ann. Polon. Math. 99 (2010), 99–105.
  9. Mikulski, W., Higher order linear connections from first order ones, Arch. Math. (Brno) 43 (2007), 285–288.
10.2478/umcsmath-2014-0008
- Full text in PDF format

Article 00PL: Spis treści
EN: Table of contents
-

- Full text in PDF format

Article 01EN: On the adjacent eccentric distance sum of graphs
1-10

HALINA BIELAK, KATARZYNA WOLSKA


Institute of Mathematics, Maria Curie-Skłodowska University 20-031 Lublin Poland

In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph G is defined as where "(v) is the eccentricity of the vertex v, deg(v) is the degree of the vertex v and is the sum of all distances from the vertex v.
  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, Macmillan London and Elsevier, New York, 1976.
  2. Gupta, S., Singh, M., Madan, A. K., Application of graph theory: Relations of eccentric connectivity index and Wiener’s index with anti-inflammatory activity, J. Math. Anal. Appl. 266 (2002), 259–268.
  3. Gupta, S., Singh, M., Madan, A. K., Eccentric distance sum: A novel graph invariant for predicting biological and physical properties, J. Math. Anal. Appl. 275 (2002), 386–401.
  4. Hua, H., Yu, G., Bounds for the Adjacent Eccentric Distance Sum, Int. Math. Forum, 7, no. 26 (2002), 1289–1294.
  5. Ilic, A., Eccentic connectivity index, Gutman, I., Furtula, B., (Eds.) Novel Molecular Structure Descriptors – Theory and Applications II, Math. Chem. Monogr., vol. 9, University of Kragujevac, 2010.
  6. Ilic, A., Yu, G., Feng, L., On eccentric distance sum of graphs, J. Math. Anal. Appl. 381 (2011), 590–600.
  7. Sardana, S., Madan, A. K., Predicting anti-HIV activity of TIBO derivatives: a computational approach using a novel topological descriptor, J. Mol. Model 8 (2000), 258–265.
  8. Yu, G., Feng, L., Ilic, A., On the eccentric distance sum of trees and unicyclic graphs, J. Math. Anal. Appl. 375 (2011), 99–107.
10.1515/umcsmath-2015-0001
- Full text in PDF format

Article 02EN: On path-quasar Ramsey numbers
11-17

BINLONG LI 1;2, BO NING 1


1 Department of Applied Mathematics Northwestern Polytechnical University Xi’an, Shaanxi 710072 P. R. China
2 Department of Mathematics University of West Bohemia Univerzitn´ı 8, 306 14 Plzeˇn, Czech Republic

Let G1 and G2 be two given graphs. The Ramsey number R(G1;G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or G contains a G2. Parsons gave a recursive formula to determine the values of R(Pn;K1;m), where Pn is a path on n vertices and K1;m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn;K1 _Fm), where Fm is a linear forest on m vertices. We determine the exact values of R(Pn;K1 _ Fm) for the cases m  n and m  2n, and for the case that Fm has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1  m  2n
  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976.
  2. Chen, Y., Zhang, Y., Zhang, K., The Ramsey numbers of paths versus wheels, Discrete Math. 290 (1) (2005), 85–87.
  3. Dirac, G. A., Some theorems on abstract graphs, Proc. London. Math. Soc. 2 (1952), 69–81.
  4. Faudree, R. J., Lawrence, S. L., Parsons, T. D., Schelp, R. H., Path-cycle Ramsey numbers, Discrete Math. 10 (2) (1974), 269–277.
  5. Graham, R. L., Rothschild, B. L., Spencer, J. H., Ramsey Theory, Second Edition, John Wiley & Sons Inc., New York, 1990.
  6. Li, B., Ning, B., The Ramsey numbers of paths versus wheels: a complete solution, Electron. J. Combin. 21 (4) (2014), #P4.41.
  7. Parsons, T. D., Path-star Ramsey numbers, J. Combin. Theory, Ser. B 17 (1) (1974), 51–58.
  8. Rousseau, C. C., Sheehan, J., A class of Ramsey problems involving trees, J. London Math. Soc. 2 (3) (1978), 392–396.
  9. Salman, A. N. M., Broersma, H. J., Path-fan Ramsey numbers, Discrete Applied Math. 154 (9) (2006), 1429–1436.
  10. Salman, A. N. M., Broersma, H. J., Path-kipas Ramsey numbers, Discrete Applied Math. 155 (14) (2007), 1878–1884.
  11. Zhang, Y., On Ramsey numbers of short paths versus large wheels, Ars Combin. 89 (2008), 11–20.
10.1515/umcsmath-2015-0002
- Full text in PDF format

Article 03EN: Rotation indices related to Poncelet’s closure theorem
19-26

WALDEMAR CIESLAK 1, HORST MARTINI 2, WITOLD MOZGAWA 3


1 Department of Applied Mathematics Lublin University of Technology ul. Nadbystrzycka 40 20-618 Lublin Poland
2 Faculty of Mathematics Technical University Chemnitz 09107 Chemnitz Germany
3 Institute of Mathematics Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1 20-031 Lublin Poland

Let CRCr denote an annulus formed by two non-concentric circles CR;Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with n- gons for any n > k.
  1. Berger, M., Geometry, I and II, Springer, Berlin, 1987.
  2. Black, W. L., Howland, H. C., Howland, B., A theorem about zigzags between two circles, Amer. Math. Monthly 81 (1974), 754–757.
  3. Bos, H. J. M., Kers, C., Dort, F., Raven, D. W., Poncelet’s closure theorem, Expo. Math. 5 (1987), 289–364.
  4. Cima, A., Gasull, A., Manosa, V., On Poncelet’s maps, Comput. Math. Appl. 60 (2010), 1457–1464.
  5. Cieslak, W., The Poncelet annuli, Beitr. Algebra Geom. 55 (2014), 301–309.
  6. Cieslak, W., Martini, H., Mozgawa, W., On the rotation index of bar billiards and Poncelet’s porism, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 287–300.
  7. Lion, G., Variational aspects of Poncelet’s theorem, Geom. Dedicata 52 (1994), 105– 118.
  8. Martini, H., Recent results in elementary geometry, Part II, Symposia Gaussiana, Proc. 2nd Gauss Symposium (Munich, 1993), de Gruyter, Berlin and New York, 1995, 419–443.
  9. Schwartz, R., The Poncelet grid, Adv. Geom. 7 (2007), 157–175.
  10. Weisstein, E. W., Poncelet’s Porism, http:/mathworld. wolfram. com/Ponceletsporism.html
10.1515/umcsmath-2015-0003
- Full text in PDF format

Article 04EN: On certain generalized q-Appell polynomial expansions
27-50

THOMAS ERNST


Department of Mathematics Uppsala University P.O. Box 480, SE-751 06 Uppsala Sweden e-mail: thomas@math.uu.se

We study q-analogues of three Appell polynomials, the H-polynomials, the Apostol–Bernoulli and Apostol–Euler polynomials, whereby two new q-difference operators and the NOVA q-addition play key roles. The definitions of the new polynomials are by the generating function; like in our book, two forms, NWA and JHC are always given together with tables, symmetry relations and recurrence formulas. It is shown that the complementary argument theorems can be extended to the new polynomials as well as to some related polynomials. In order to find a certain formula, we introduce a q-logarithm. We conclude with a brief discussion of multiple q-Appell polynomials.
  1. Apostol, T. M., On the Lerch zeta function, Pacific J. Math. 1 (1951), 161–167.
  2. Dere, R., Simsek, Y., Srivastava, H. M., A unified presentation of three families of generalized Apostol type polynomials based upon the theory of the umbral calculus and the umbral algebra, J. Number Theory 133, no. 10 (2013), 3245–3263.
  3. Ernst, T., A comprehensive treatment of q-calculus, Birkh¨auser, Basel, 2012.
  4. Ernst, T., q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials, J. Discrete Math. 2013.
  5. Jordan, Ch., Calculus of finite differences, Third Edition, Chelsea Publishing Co., New York, 1950.
  6. Kim M., Hu S., A note on the Apostol–Bernoulli and Apostol–Euler polynomials, Publ. Math. Debrecen 5587 (2013), 1–16.
  7. Lee, D. W., On multiple Appell polynomials, Proc. Amer. Math. Soc. 139, no. 6 (2011), 2133–2141.
  8. Luo, Q.-M., Srivastava, H. M., Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials, J. Math. Anal. Appl. 308, no. 1 (2005), 290–302.
  9. Luo, Q.-M., Srivastava, H. M., Some relationships between the Apostol–Bernoulli and Apostol–Euler polynomials, Comput. Math. Appl. 51, no. 3–4 (2006), 631–642.
  10. Luo, Q.-M., Apostol–Euler polynomials of higher order and Gaussian hypergeometric functions, Taiwanese J. Math. 10, no. 4 (2006), 917–925.
  11. Milne-Thomson, L. M., The Calculus of Finite Differences, Macmillan and Co., Ltd., London, 1951.
  12. Nørlund, N. E., Differenzenrechnung, Springer-Verlag, Berlin, 1924.
  13. Pint´er, ´A, Srivastava, H. M., Addition theorems for the Appell polynomials and the associated classes of polynomial expansions, Aequationes Math. 85, no. 3 (2013), 483–495.
  14. Sandor, J., Crstici, B., Handbook of number theory II, Kluwer Academic Publishers, Dordrecht, 2004.
  15. Srivastava, H. M., ¨ Ozarslan, M. A., Kaanoglu, C., Some generalized Lagrange-based Apostol–Bernoulli, Apostol–Euler and Apostol–Genocchi polynomials, Russ. J. Math. Phys. 20, no. 1 (2013), 110–120.
  16. Wang, W., Wang, W., Some results on power sums and Apostol-type polynomials, Integral Transforms Spec. Funct. 21, no. 3–4 (2010), 307–318.
  17. Ward, M., A calculus of sequences, Amer. J. Math. 58 (1936), 255–266.
10.1515/umcsmath-2015-0004
- Full text in PDF format

Article 05EN: Deviation from weak Banach–Saks property for countable direct sums
51-58

ANDRZEJ KRYCZKA


Institute of Mathematics Maria Curie-Skłodowska University 20-031 Lublin Poland e-mail: andrzej.kryczka@umcs.pl

We introduce a seminorm for bounded linear operators between Banach spaces that shows the deviation from the weak Banach–Saks property. We prove that if (X) is a sequence of Banach spaces and a Banach sequence lattice E has the Banach–Saks property, then the deviation from the weak Banach–Saks property of an operator of a certain class between direct sums E(X) is equal to the supremum of such deviations attained on the coordinates X. This is a quantitative version for operators of the result for the K¨othe– Bochner sequence spaces E(X) that if E has the Banach–Saks property, then E(X) has the weak Banach–Saks property if and only if so has X.
  1. Banach, S., Saks, S., Sur la convergence forte dans les champs Lp, Studia Math. 2 (1930), 51–57.
  2. Beauzamy, B., Banach–Saks properties and spreading models, Math. Scand. 44 (1979), 357–384.
  3. Brunel, A., Sucheston, L., On B-convex Banach spaces, Math. Systems Theory 7 (1974), 294–299.
  4. Erd¨os, P., Magidor, M., A note on regular methods of summability and the Banach– Saks property, Proc. Amer. Math. Soc. 59 (1976), 232–234.
  5. Krassowska, D., Płuciennik, R., A note on property (H) in K¨othe–Bochner sequence spaces, Math. Japon. 46 (1997), 407–412.
  6. Krein, S. G., Petunin, Yu. I., Semenov, E. M., Interpolation of linear operators, Translations of Mathematical Monographs, 54. American Mathematical Society, Providence, R.I., 1982.
  7. Kryczka, A., Alternate signs Banach–Saks property and real interpolation of operators, Proc. Amer. Math. Soc. 136 (2008), 3529–3537.
  8. Kryczka, A., Mean separations in Banach spaces under abstract interpolation and extrapolation, J. Math. Anal. Appl. 407 (2013), 281–289.
  9. Lin, P.-K., K¨othe–Bochner function spaces, Birkh¨auser Boston, Inc., Boston, MA, 2004.
  10. Lindenstrauss, J., Tzafriri, L., Classical Banach spaces. II. Function spaces, Springer- Verlag, Berlin–New York, 1979.
  11. Mastyło, M., Interpolation spaces not containing l1, J. Math. Pures Appl. 68 (1989), 153–162.
  12. Partington, J. R., On the Banach–Saks property, Math. Proc. Cambridge Philos. Soc. 82 (1977), 369–374.
  13. Rosenthal, H. P., Weakly independent sequences and the Banach–Saks property, Bull. London Math. Soc. 8 (1976), 22–24.
  14. Szlenk, W., Sur les suites faiblement convergentes dans l’espace L, Studia Math. 25 (1965), 337–341.
10.1515/umcsmath-2015-0005
- Full text in PDF format

Article 06EN: The natural transformations between r-tangent and r-cotangent bundles over Riemannian manifolds
59-64

JAN KUREK 1, WŁODZIMIERZ M. MIKULSKI 2


1 Institute of Mathematics Maria Curie-Skłodowska University pl. Marii Curie-Skłodowskiej 1 20-031 Lublin Poland
2 Institute of Mathematics Jagiellonian University ul. S. Łojasiewicza 6 30-348 Kraków Poland

If (M; g) is a Riemannian manifold, we have the well-known base preserving vector bundle isomorphism TM ~= TM given by v ! g(v;
  1. Epstein, D. B. A., Natural tensors on Riemannian manifolds, J. Diff. Geom. 10 (1975), 631–645.
  2. Kobayashi, S., Nomizu, K., Foundations of Differential Geometry. Vol. I, J. Wiley- Interscience, New York–London, 1963.
  3. Kol´aˇr, I., Michor, P. W., Slov´ak, J., Natural Operations in Defferential Geometry, Springer-Verlag, Berlin, 1993.
  4. Kol´aˇr, I., Vosmansk´a, G., Natural transformations of higher order tangent bundles and jet spaces, ˇCas. pˇest. mat. 114 (1989), 181–186.
  5. Kurek, J., Natural transformations of higher order cotangent bundle functors, Ann. Polon. Math. 58, no. 1 (1993), 29–35.
  6. Mikulski, W. M., Some natural operators on vector fields, Rend Math. Appl (7) 12, no. 3 (1992), 783–803.
  7. Nijenhuis, A., Natural bundles and their general properties Diff. Geom. in Honor of K. Yano, Kinokuniya, Tokyo (1972), 317–334.
  8. Paluszny, M., Zajtz, A., Foundation of the Geometry of Natural Bundles, Lect. Notes Univ. Caracas, 1984.
10.1515/umcsmath-2015-0006
- Full text in PDF format

Article 07EN: On certain subclasses of analytic functions associated with the Carlson–Shaffer operator
65-83

JAGANNATH PATEL 1, ASHOK KUMAR SAHOO 2


1 Department of Mathematics Utkal University Vani Vihar, Bhubaneswar-751004 India e-mail: jpatelmath@yahoo.co.in
2 Department of Mathematics Veer Surendra Sai University of Technology Sidhi Vihar, Burla-768018 India e-mail: ashokuumt@gmail.com

The object of the present paper is to solve Fekete–Szeg¨o problem and determine the sharp upper bound to the second Hankel determinant for a certain class R(a; c; A;B) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass Re(a; c; A;B) of R(a; c; A;B) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.
  1. Altinta¸s, O., ¨Ozkan, O., Srivastava, H. M., Majorization by starlike functions of complex order, Complex Var. 46 (2001), 207–218.
  2. Caplinger, T. R., Causey, W. M., A class of univalent functions, Proc. Amer. Math. Soc. 39 (1973), 357–361.
  3. Carlson, B. C., Shaffer, D. B., Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737–745.
  4. Duren, P. L., Univalent Functions, Grundlehren der MathematischenWissenschaften, 259, Springer-Verlag, New York, USA, 1983.
  5. Fekete, M., Szeg¨o, G., Eine Bemerkung ¨uber ungerede schlichte funktionen, J. London Math. Soc. 8 (1933), 85–89.
  6. Goyal, S. P., Goswami, P., Majorization for certain subclass of analytic functions defined by linear operator using differential subordination, Appl. Math. Letters 22 (2009), 1855–1858.
  7. Goyal, S. P., Bansal, S. K., Goswami, P., Majorization for certain classes of functions by fractional derivatives, J. Appl. Math. Stat. Informatics 6(2) (2010), 45–50.
  8. Janteng, A., Halim, S. A., Darus, M., Coefficient inequality for a function whose derivative has a positive real part, J. Inequal. Pure Appl. Math. 7 (2006), Art. 50 [http://jipam.vu.edu.au/].
  9. Janteng, A., Halim, S. A., Darus, M., Estimate on the second Hankel functional for functions whose derivative has a positive real part, J. Quality Measurement and Analysis 4 (2008), 189–195.
  10. Juneja, O. P., Mogra, M. L., A class of univalent functions, Bull. Sci. Math. (2) 103 (1979), 435–447.
  11. Keogh, F. R., Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12.
  12. Koepf, W., On the Fekete-Szeg¨o problem for close-to-convex functions. II, Arch. Math. (Basel) 49 (1987), 420–433.
  13. Koepf, W., On the Fekete-Szeg¨o problem for close-to-convex functions, Proc. Amer. Math. Soc. 101 (1987), 89–95.
  14. Libera, R. J., Złotkiewicz, E. J., Early coefficient of the inverse of a regular convex function, Proc. Amer. Math. Soc. 85 (2) (1982), 225–230.
  15. Libera, R. J., Złotkiewicz, E. J., Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2) (1983), 251–257.
  16. Ma, W. C., Minda, D., A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Z. Li, F. Ren, L. Yang and S. Zhang (Eds.), Int. Press, Cambridge, MA, 1994, 157–169.
  17. MacGregor, T. H., Functions whose derivative have a positive real part, Trans. Amer. Math. Soc. 104(3) (1962), 532–537.
  18. MacGregor, T. H., The radius of univalence of certain analytic functions, Proc. Amer. Math. Soc. 14 (1963), 514–520.
  19. MacGregor, T. H., Majorization by univalent functions, Duke Math. J. 34 (1967), 95–102.
  20. Miller, S. S., Mocanu, P. T., Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York and Basel, 2000.
  21. Mishra, A. K., Kund, S. N., The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator, Tamkang J. Math. 44(1) (2013), 73–82.
  22. Nehari, Z., Conformal Mapping, McGraw-Hill Book Company, New York, Toronto and London, 1952.
  23. Noonan, J. W., Thomas, D. K., On the second Hankel determinant of areally mean p-valent functions, Trans. Amer. Math. Soc. 223 (1976), 337–346.
  24. Noor, K. I., Hankel determinant problem for the class of functions with bounded boundary rotation, Rev. Roum. Math. Pures Appl. 28 (1983), no. 8, 731–739.
  25. Owa, S., Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (1987), 1057–1077.
  26. Ruscheweyh, St., New criteria for univalent functions, Proc. Amer. Math. Soc. 49 (1975), 109–115.
  27. Silverman, H., Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109–116.
  28. Srivastava, H. M., Karlson, P. W., Karlsson, Per W., Multiple Gaussian Hypergeometric Series (Mathematics and its Applications), A Halsted Press Book (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
10.1515/umcsmath-2015-0007
- Full text in PDF format

Article 08EN: Renormings of c0 and the minimal displacement problem
85-91

ŁUKASZ PIASECKI


Institute of Mathematics Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1 20-031 Lublin Poland e-mail: piasecki@hektor.umcs.lublin.pl

The aim of this paper is to show that for every Banach space (X; k  k) containing asymptotically isometric copy of the space c0 there is a bounded, closed and convex set C  X with the Chebyshev radius r(C) = 1 such that for every k  1 there exists a k-contractive mapping T : C ! C with kx
  1. Bolibok, K., The minimal displacement problem in the space l1, Cent. Eur. J. Math. 10 (2012), 2211–2214.
  2. Bolibok, K., Constructions of lipschitzian mappings with non zero minimal displacement in spaces L1 (0; 1) and L2 (0; 1), Ann. Univ. Mariae Curie-Skłodowska Sec. A 50 (1996), 25–31.
  3. Dowling, P. N., Lennard C. J., Turett, B., Reflexivity and the fixed point property for nonexpansive maps, J. Math. Anal. Appl. 200 (1996), 653–662.
  4. Dowling, P. N., Lennard, C. J., Turett, B., Some fixed point results in l1 and c0, Nonlinear Anal. 39 (2000), 929–936.
  5. Dowling, P. N., Lennard C. J., Turett , B., Asymptotically isometric copies of c0 in Banach spaces, J. Math. Anal. Appl. 219 (1998), 377–391.
  6. Goebel, K., On the minimal displacement of points under lipschitzian mappings, Pacific J. Math. 45 (1973), 151–163.
  7. Goebel, K., Concise Course on Fixed Point Theorems, Yokohama Publishers, Yokohama, 2002.
  8. Goebel, K., Kirk, W. A., Topics in metric fixed point theory, Cambridge University Press, Cambridge, 1990.
  9. Goebel, K., Marino, G., Muglia, L., Volpe, R., The retraction constant and minimal displacement characteristic of some Banach spaces, Nonlinear Anal. 67 (2007), 735– 744.
  10. James, R. C., Uniformly non-square Banach spaces, Ann. of Math. 80 (1964), 542– 550.
  11. Kirk, W. A., Sims, B. (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dordrecht, 2001.
  12. Lin, P. K., Sternfeld, Y., Convex sets with the Lipschitz fixed point property are compact, Proc. Amer. Math. Soc. 93 (1985), 633–639.
  13. Piasecki, Ł., Retracting a ball onto a sphere in some Banach spaces, Nonlinear Anal. 74 (2011), 396–399.
10.1515/umcsmath-2015-0008
- Full text in PDF format

Volume 67 - 2013

Article 01EN: On lifts of projectable-projectable classical linear connections to the cotangent bundle
1-10

Anna Bednarska


Institute of Mathematics Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1 20-031 Lublin Poland e-mail: bednarska@hektor.umcs.lublin.pl

We describe all F2Mm1;m2;n1;n2-natural operators D: Q_(proj-proj)^T →QT* transforming projectable-projectable classical torsion-free linear connections ∇ on fibred-fibred manifolds Y into classical linear connections D(∇) on cotangent bundles T*Y of Y . We show that this problem can be reduced to finding F2Mm1,m2,n1,n2 -natural operators D: QTproj-proj → (T*⊗pT* ⊗⊗q T) for p=2, q=1 and p=3, q=0.
  1. Doupovec, M., Mikulski, W. M., On prolongation of higher order connections, Ann. Polon. Math. 102, no. 3 (2011), 279–292.
  2. Kolár, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 59 (2005), 67–76.
  3. Kolár, I., Michor, P. W., Slovák, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin–Heidelberg, 1993.
  4. Kurek, J., Mikulski, W. M., On prolongations of projectable
  5. Kurek, J., Mikulski, W. M., The natural liftings of connections to tensor powers of the cotangent bundle, AGMP-8 Proceedings (Brno 2012), Miskolc Mathematical Notes, to appear.
  6. Kurés, M., Natural lifts of classical linear connections to the cotangent bundle, Suppl. Rend. Mat. Palermo II 43 (1996), 181–187.
  7. Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (3–4) (2001), 441–458.
  8. Yano, K., Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker, Inc., New York, 1973.
10.2478/v10062-012-0017-x
- Full text in SWF PDF format

Article 02EN: Generalization of some extremal problems on non-overlapping domains with free poles
11-22

Iryna V. Denega


Department of Complex Analysis and Potential Theory Institute of Mathematics of National Academy of Sciences of Ukraine Tereshchenkivska St. 3 01601 Kyiv Ukraine e-mail: iradenega@yandex.ru

Some results related to extremal problems with free poles on radial systems are generalized. They are obtained by applying the known methods of geometric function theory of complex variable. Sufficiently good numerical results for ⋎ are obtained.
  1. Bieberbach, L., Über die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitzungsber. Preuss. Akad. Wiss. Phys- Math. Kl. 138 (1916), 940–955.
  2. Bakhtin, A. K., Bakhtina, G. P., Separating transformation and problem on nonoverlapping domains, Proceedings of Institute of Mathematics of NAS of Ukraine 3 (4) (2006), 273–281.
  3. Bakhtin, A. K., Bakhtina, G. P., Zelinskii, Yu. B., Topological-algebraic structures and geometric methods in complex analysis, Proceedings of the Institute of Mathematics of NAS of Ukraine 73 (2008), 308 pp. (Russian).
  4. Dubinin, V. N., The symmetrization method in problems on non-overlapping domains, Mat. Sb. (N.S.) 128 (1) (1985), 110–123 (Russian).
  5. Dubinin, V. N., A separating transformation of domains and problems on extremal decomposition, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 168 (1988), 48–66 (Russian); translation in J. Soviet Math. 53, no. 3 (1991), 252–263.
  6. Dubinin, V. N., Symmetrization method in geometric function theory of complex variables, Uspekhi Mat. Nauk 49, no. 1 (1994), 3–76 (Russian); translation in Russian Math. Surveys 49, no. 1 (1994), 1–79.
  7. Dubinin, V. N., Asymptotics of the modulus of a degenerate condenser, and some of its applications, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 237 (1997), 56–73 (Russian); translation in J. Math. Sci. (New York) 95, no. 3 (1999), 2209–2220.
  8. Dubinin, V. N., Capacities of condensers and symmetrization in geometric function theory of complex variables, Dal’nayka, Vladivostok, 2009 (Russian).
  9. Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983. [10] Goluzin, G. M., Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, no. 26, Amer. Math. Soc., Providence, R.I. (1969).
  10. Gr¨otzsch, H., ¨ Uber einige Extremalprobleme der konformen Abbildung. I, II, Ber. Verh. S¨achs. Akad. Wiss. Leipzig, Math.-Phys. 80 (6) (1928), 367–376, 497–502.
  11. Grunsky, H., Koeffizientenbedingungen f¨ur schlicht abbildende meromorphe Funltionen, Math. Z. 45, no. 1 (1939), 29–61.
  12. Hayman, W. K., Multivalent Functions, Cambridge University Press, Cambridge, 1958.
  13. Jenkins, J. A., Some uniqueness results in the theory of symmetrization, Ann. Math. 61, no. 1 (1955), 106–115.
  14. Kolbina, L. I., Conformal mapping of the unit circle onto non-overlapping domains, Vestnik Leningrad. Univ. 10, no. 5 (1955), 37–43 (Russian).
  15. Kovalev, L. V., On the problem of extremal decomposition with free poles on the circle, Dal’nevost. Mat. Sb. 2 (1996), 96–98 (Russian).
  16. Lavrent’ev, M. A., On the theory of conformal mappings, Tr. Fiz.-Mat. Inst. Akad. Nauk SSSR, Otdel. Mat. 5 (1934), 195–245 (Russian).
  17. Nehari, Z., Some inequalities in the theory of functions Trans. Amer. Math. Soc. 75, no. 2 (1953), 256–286.
  18. Riemann, B., Theorie der Abelschen Functionen J. Reine Angew. Math. 54 (1867), 101–155.
  19. Teichmüller, O., Collected Papers, Springer, Berlin, 1982.
  20. Vasil’ev, A., Moduli of Families of Curves for Conformal and Quasiconformal Mappings, Springer-Verlag, Berlin, 2002.
10.2478/v10062-012-0018-9
- Full text in SWF PDF format

Article 03EN: Spacelike intersection curve of three spacelike hypersurfaces in E4
23-33

B. Uyar Düldül 1, M. Çalişkan 2


1 Department of Mathematics Education Education Faculty Yıldız Technical University Istanbul Turkey e-mail: buduldul@yildiz.edu.tr
2 Department of Mathematics Science Faculty Gazi University Ankara Turkey e-mail: mustafacaliskan@gazi.edu.tr

In this paper, we compute the Frenet vectors and the curvatures of the spacelike intersection curve of three spacelike hypersurfaces given by their parametric equations in four-dimensional Minkowski space E14 .
  1. Alessio, O., Geometria diferencial de curvas de interse¸c˜ao de duas superf´ıcies impl´ıcitas, TEMA Tend. Mat. Apl. Comput. 7 (2) (2006), 169–178.
  2. Alessio, O., Guadalupe, I. V., Determination of a transversal intersection curve of two spacelike surfaces in Lorentz–Minkowski 3-Space L3, Hadronic Journal 30 (3) (2007), 315–342.
  3. Alessio, O., Differential geometry of intersection curves in R4 of three implicit surfaces, Comput. Aided Geom. Des. 26 (2009), 455–471.
  4. D¨uld¨ul, M., On the intersection curve of three parametric hypersurfaces, Comput. Aided Geom. Des. 27 (2010), 118–127.
  5. Goldman, R., Curvature formulas for implicit curves and surfaces, Comput. Aided Geom. Des. 22 (2005), 632–658.
  6. Hartmann, E., G2 interpolation and blending on surfaces, The Visual Computer 12 (1996), 181–192.
  7. Turgut, A., Spacelike and timelike ruled surfaces on the Minkowski 3-space R3 1, Ph. D. thesis, Ankara University, 1995.
  8. O’Neill, B., Semi Riemannian Geometry, Academic Press, New York–London, 1983.
  9. Walrave, J., Curves and surfaces in Minkowski space, Ph. D. thesis, K. U. Leuven. Fac. Science, Leuven, 1995.
  10. Williams, M. Z., Stein, F. M., A triple product of vectors in four-space, Math. Mag. 37 (4) (1964), 230–235.
  11. Willmore, T. J., An Introduction to Differential Geometry, Clarendon Press, Oxford, 1959.
  12. Ye, X., Maekawa T., Differential geometry of intersection curves of two surfaces, Comput. Aided Geom. Des. 16 (1999), 767–788.
  13. Yilmaz, S., Turgut, M., On the differential geometry of the curves in Minkowski space-time I, Int. J. Contemp. Math. Sciences 3 (27) (2008), 1343–1349.
10.2478/v10062-012-0019-8
- Full text in SWF PDF format

Article 04EN: Trace parameters for Teichmüller space of genus 2 surfaces and mapping class group
35-44

Gou Nakamura 1, Toshihiro Nakanishi 2


1 Science Division, Center for General Education Aichi Institute of Technology 1247 Yachigusa, Yakusa, Toyota 470-0392, Japan e-mail: gou@aitech.ac.jp
2 Department of Mathematics, Shimane University Matue, 690-8504, Japan e-mail: tosihiro@riko.shimane-u.ac.jp

We obtain a representation of the mapping class group of genus 2 surface in terms of a coordinate system of the Teichm¨uller space defined by trace functions.
  1. Birman, J. S., Braids, links, and mapping class groups, Ann. of Math. Studies 82, Princeton Univ. Press, Princeton, N. J., 1974.
  2. Maclachlan, C., Reid, A. W., The Arithmetic of Hyperbolic 3-Manifolds, Springer- Verlag, New York, 2003.
  3. Nakamura, G., Nakanishi, T., Parametrizations of some Teichm¨uller spaces by trace functions, Conform. Geom. Dyn. 17 (2013), 47–57.
  4. Nakanishi, T., Näätänen, M., Parametrization of Teichmüller space by length parameters, Analysis and Topology (C. Andreian-Cazacu, O. Lehto and Th. M. Rassias, eds.), 541–560, World Sci. Publ., Singapore, 1998.
  5. Zieschang, H., Finite Groups of Mapping Classes of Surfaces, Springer-Verlag, Berlin, 1981.
10.2478/v10062-012-0020-2
- Full text in SWF PDF format

Article 05EN: Linearly-invariant families and generalized Meixner–Pollaczek polynomials
45-56

Iwona Naraniecka 1, Jan Szynal 2, Anna Tatarczak 3


1 Department of Mathematics Faculty of Economics Maria Curie-Skłodowska University 20-031 Lublin Poland e-mail: inaraniecka@gmail.com
2 University of Economics and Innovation in Lublin 20-209 Lublin Poland e-mail: jan.szynal3@gmail.com
3 Department of Mathematics Faculty of Economics Maria Curie-Skłodowska University 20-031 Lublin Poland e-mail: antatarczak@gmail.com

The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f’(z) ) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f_0^'(z) looks similar to generating function for Meixner–Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner–Pollaczek (GMP) polynomials P_n^λ (x;θ,ψ)zn of a real variable x as coefficients of G_^λ (x;θ,ψ,z) =1/(〖〖(1-ze〗_^iθ)〗_^(λ-ix) 〖〖(1-ze〗_^iψ)〗_^(λ+ix) ) = ∑_(n=0)^∞▒P_n^λ (x; θ,
  1. Araaya, T. K., The symmetric Meixner–Pollaczek polynomials, Uppsala Dissertations in Mathematics, Department of Mathematics, Uppsala University, 2003.
  2. Chihara, T. S., An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
  3. Duren, P. L., Univalent Functions, Springer, New York, 1983.
  4. Erd´elyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Higher Transcendental Functions, vol. I, McGraw-Hill Book Company, New York, 1953.
  5. Golusin, G., Geometric Theory of Functions of a Complex Variable, Translations of Mathematical Monographs, no. 26, Amer. Math. Soc., Providence, R.I., 1969.
  6. Ismail, M., On sieved ultraspherical polynomials I: Symmetric Pollaczek analogues, SIAM J. Math. Anal. 16 (1985), 1093–1113.
  7. Kiepiela, K., Naraniecka, I., Szynal, J., The Gegenbauer polynomials and typically real functions, J. Comp. Appl. Math 153 (2003), 273–282.
  8. Koekoek, R., Swarttouw, R. F., The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Report 98-17, Delft University of Technology, 1998.
  9. Koornwinder, T. H., Meixner–Pollaczek polynomials and the Heisenberg algebra, J. Math. Phys. 30 (4) (1989), 767–769.
  10. Pommerenke, Ch., Linear-invariant Familien analytischer Funktionen, Mat. Ann. 155 (1964), 108–154.
  11. Poularikas, A. D., The Mellin Transform, The Handbook of Formulas and Tables for Signal Processing, CRC Press LLC, Boca Raton, 1999.
  12. Robertson, M. S., On the coefficients of typically-real functions, Bull. Amer. Math. Soc. 41 (1935), 565–572.
  13. Rogosinski, W. W., ¨ Uber positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Z. 35 (1932), 93–121.
  14. Starkov, V. V., The estimates of coefficients in locally-univalent family U 0_, Vestnik Lenin. Gosud. Univ. 13 (1984), 48–54 (Russian).
  15. Starkov, V. V., Linear-invariant families of functions, Dissertation, Ekatirenburg, 1989, 1–287 (Russian).
  16. Szynal, J., An extension of typically-real functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 48 (1994), 193–201.
  17. Szynal, J., Waniurski, J., Some problems for linearly invariant families, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 30 (1976), 91–102.
10.2478/v10062-012-0021-1
- Full text in SWF PDF format

Article 06EN: On limiting values of Cauchy type integral in a harmonic algebra with two-dimensional radical
57-64

S. A. Plaksa 1, V. S. Shpakivskyi 2


1 Department of Complex Analysis and Potential Theory Institute of Mathematics of the National Academy of Sciences of Ukraine Tereshchenkivska St. 3 01601 Kiev-4 Ukraine e-mail: plaksa@imath.kiev.ua
2 Department of Complex Analysis and Potential Theory Institute of Mathematics of the National Academy of Sciences of Ukraine Tereshchenkivska St. 3 01601 Kiev-4 Ukraine e-mail: shpakivskyi@mail.ru

We consider a certain analog of Cauchy type integral taking values in a three-dimensional harmonic algebra with two-dimensional radical. We establish sufficient conditions for an existence of limiting values of this integral on the curve of integration.
  1. Davydov, N. A., The continuity of an integral of Cauchy type in a closed domain, Dokl. Akad. Nauk SSSR 64, no. 6 (1949), 759–762 (Russian).
  2. Salaev, V. V., Direct and inverse estimates for a singular Cauchy integral along a closed curve, Mat. Zametki 19, no. 3 (1976), 365–380 (Russian).
  3. Gerus, O. F., Finite-dimensional smoothness of Cauchy-type integrals, Ukrainian Math. J. 29, no. 5 (1977), 490–493.
  4. Gerus, O. F., Some estimates of moduli of smoothness of integrals of the Cauchy type, Ukrainian Math. J. 30, no. 5 (1978), 594–601.
  5. Ketchum, P. W., Analytic functions of hypercomplex variables, Trans. Amer. Math. Soc. 30 (1928), 641–667.
  6. Kunz, K. S., Application of an algebraic technique to the solution of Laplace’s equation in three dimensions, SIAM J. Appl. Math. 21, no. 3 (1971), 425–441. [7] Mel’nichenko, I. P., The representation of harmonic mappings by monogenic functions, Ukrainian Math. J. 27, no. 5 (1975), 499–505.
  7. Mel’nichenko, I. P., Algebras of functionally invariant solutions of the threedimensional Laplace equation, Ukrainian Math. J. 55, no. 9 (2003), 1551–1559.
  8. Mel’nichenko, I. P., Plaksa, S. A., Commutative algebras and spatial potential fields, Inst. Math. NAS Ukraine, Kiev, 2008 (Russian).
  9. Plaksa, S. A., Riemann boundary-value problem with infinite index of logarithmic order on a spiral contour. I, Ukrainian Math. J. 42, no. 11 (1990), 1509–1517.
  10. Shpakivskyi, V. S., Plaksa, S. A., Integral theorems and a Cauchy formula in a commutative three-dimensional harmonic algebra, Bull. Soc. Sci. Lett. Łódz Sér. Rech. Déform. 60 (2010), 47–54.
10.2478/v10062-012-0022-0
- Full text in SWF PDF format

Article 07EN: On boundary behavior of Cauchy integrals
65-82

Hiroshige Shiga


Department of Mathematics Tokyo Institute of Technology e-mail: shiga@math.titech.ac.jp

In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj–Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
  1. Aikawa, H., Modulus of continuity of the Dirichlet solutions, Bull. London Math. Soc. 42 (2010), 857–867.
  2. Bikˇcantaev, I. A., Analogues of a Cauchy kernel on a Riemann surface and some applications of them, Mat. Sb. (N.S.) 112 (154), no. 2 (6) (1980), 256–282 (Russian); translation in Math. USSR Sb. 40, no. 2 (1981), 241–265.
  3. Block, I. E., The Plemelj theory for the class __ of functions, Duke Math. J. 19 (1952), 367–378.
  4. Duren, P. L., Theory of Hp Spaces, Academic Press, New York–San Francisco–London, 1970.
  5. Farkas, H. M., Kra, I., Riemann Surfaces, Springer-Verlag, New York–Heidelberg–Berlin, 1980.
  6. Gakhov, F. D., Boundary Value Problems, Pergamon Press, Oxford–New York–Paris, 1966.
  7. Garnett, J. B., Bounded Analytic Functions, Academic Press, New York–London, 1981.
  8. Gong, S., Integrals of Cauchy type on the ball, International Press, Cambridge, 1993.
  9. Guseinov, E. G., The Plemelj-Privalov theorem for generalized H¨older classes, Mat. Sb. 183, no. 2 (1992), 21–37 (Russian); translation in Russian Acad. Sci. Sb. Math. 75 (1993), 165–182.
  10. Heins, M., Hardy Classes on Riemann Surfaces, Springer-Verlag, Berlin–New York, 1969.
  11. Shiga, H., Riemann mappings of invariant components of Kleinian groups, J. London Math. Soc. 80 (2009), 716–728.
  12. Shiga, H., Modulus of continuity, a Hardy–Littlewood theorem and its application, RIMS Kokyuroku Bessatsu, 2010, 127–133.
  13. Pommerenke, C., Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992.
  14. Walsh, J. L., Polynomial expansions of functions defined by Cauchy’s integral, J. Math. Pures Appl. 31 (1952), 221–244.
10.2478/v10062-012-0023-z
- Full text in SWF PDF format

Article 08EN: Elementary examples of Loewner chains generated by densities
83-101

Alan Sola


Department of Pure Mathematics and Mathematical Statistics University of Cambridge Wilberforce Road Cambridge, CB3 0WB UK e-mail: a.sola@statslab.cam.ac.uk

We study explicit examples of Loewner chains generated by absolutely continuous driving measures, and discuss how properties of driving measures are reflected in the shapes of the growing Loewner hulls.
  1. Berkson, E., Porta, H., Semigroups of analytic functions and composition operators, Michigan Math. J. 25 (1978), 101–115.
  2. Bracci, F., Contreras, M. D., D´ıaz-Madrigal, S., Evolution families and the Loewner equation I: the unit disk, J. Reine Angew. Math., to appear.
  3. Bracci, F., Contreras, M. D., D´ıaz-Madrigal, S., Regular poles and _-numbers in the theory of holomorphic semigroups, arxiv.org/abs/1201.4705.
  4. Carleson, L., Makarov, N., Aggregation in the plane and Loewner’s equation, Comm. Math. Phys. 216 (2001), 583–607.
  5. Carleson, L., Makarov, N., Laplacian path models. Dedicated to the memory of Thomas H. Wolff, J. Anal. Math. 87 (2002), 103–150.
  6. Contreras, M. D., D´ıaz-Madrigal, S., Gumenyuk, P., Geometry behind Loewner chains, Complex Anal. Oper. Theory 4 (2010), 541–587.
  7. Contreras, M. D., D´ıaz-Madrigal, S., Gumenyuk, P., Local duality in Loewner equations, arxiv.org/abs/1202.2334.
  8. Contreras, M. D., D´ıaz-Madrigal, S., Pommerenke, Ch., On boundary critical points for semigroups of analytic functions, Math. Scand. 98 (2006), 125–142.
  9. Dur´an, M. A., Vasconcelos, G. L., Interface growth in two dimensions: A Loewner equation approach, Phys. Rev. E 82 (2010), 031601.
  10. Elin, M., Shoikhet, D., Linearization Models for Complex Dynamical Systems, Birkh¨auser Verlag, Basel, 2010.
  11. Gubiec, T., Szymczak, P., Fingered growth in channel geometry: A Loewner equation approach, Phys. Rev. E 77 (2008), 041602.
  12. Hastings, M., Levitov, L., Laplacian growth as one-dimensional turbulence, Phys. D: Nonlinear Phenomena 116 (1998), 244–252.
  13. Ivanov, G., Prokhorov, D., Vasil’ev, A., Singular solutions to the Loewner equation, Bull. Sci. Math. 136 (2012), 328–341.
  14. Johansson Viklund, F., Sola, A., Turner, A., Scaling limits of anisotropic Hastings-Levitov clusters, Ann. Inst. H. Poincar´e Probab. Stat. 48 (2012), 235–257.
  15. Kager, W., Nienhuis, B., Kadanoff, L. P., Exact solutions for Loewner evolutions, J.Statist. Phys. 115 (2004), 805–822.
  16. Kuznetsov, A., Boundary behaviour of Loewner chains, arxiv.org/abs/0705.4564. [17] Lawler, G., Conformally Invariant Processes in the Plane, American Mathematical Society, Providence, 2005.
  17. Lind, J., A sharp condition for the Loewner equation to generate slits, Ann. Acad. Sci. Fenn. Math. 30 (2005), 143–158.
  18. Lind, J., Marshall, D. E., Rohde, S., Collisions and spirals of Loewner traces, Duke Math. J. 154 (2010), 527–573.
  19. Marshall, D. E., Rohde, S., The Loewner differential equation and slit mappings, J.Amer. Math. Soc. 18 (2005), 763–778.
  20. Pommerenke, Ch., Univalent Functions, Vandenhoeck & Ruprecht, G¨ottingen, 1975.
  21. Pommerenke, Ch., Boundary Behavior of Conformal Maps, Springer-Verlag, Berlin–Heidelberg, 1992.
  22. Popescu, M. N., Hentschel, H. G. E., Family, F., Anisotropic diffusion-limited aggregation, Phys. Rev. E 69 (2004), 061403.
  23. Rohde, S., Zinsmeister, M., Some remarks on Laplacian growth, Topology Appl. 152 (2005), 26–43.
  24. Selander, G., Two deterministic growth models related to diffusion-limited aggregation. Doctoral dissertation, Thesis (Dr. Tech.), Kungliga Tekniska Hogskolan, 1999, pp. 101.
  25. Siskakis, A. G., Semi-groups of composition operators on spaces of analytic functions, a review, Studies on composition operators (Laramie, WY, 1996), 229–252, Contemp. Math., 213, Amer. Math. Soc., Providence, R.I., 1998.
  26. Vasil’ev, A., Evolution of conformal maps with quasiconformal extensions, Bull. Sci. Math. 129 (2005), 831–859.
10.2478/v10062-012-0024-y
- Full text in SWF PDF format

Article 01EN: Location of the critical points of certain polynomials
1-9

SOMJATE CHAIYA 1, AIMO HINKKANEN 2


1 Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Pathom 73000 Thailand; Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand e-mail: somjate.c@su.ac.th
2 Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green St., Urbana, IL 61801, U.S.A. e-mail: aimo@math.uiuc.edu

Let D denote the unit disk {z : |z|<1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D. We establish criteria for P to satisfy implying that each of P and P0 has exactly one critical point outside D.
  1. Boyd, D. W., Small Salem numbers, Duke Math. J. 44 (1977), 315–328.
  2. Bertin, M. J., Decomps-Guilloux, A., Grandet-Hugot, M., Pathiaux-Delefosse, M., Schreiber, J. P., Pisot and Salem Numbers, Birkh¨auser Verlag, Basel, 1992.
  3. Chaiya, S., Complex dynamics and Salem numbers, Ph.D. Thesis, University of Illinois at Urbana–Champaign, 2008.
  4. Palka, Bruce P., An Introduction to Complex Function Theory, Springer-Verlag, New York, 1991.
  5. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.
  6. Salem, R., Power series with integral coefficients, Duke Math. J. 12 (1945), 153–173.
  7. Salem, R., Algebraic Numbers and Fourier Analysis, D. C. Heath and Co., Boston, Mass., 1963.
  8. Sheil-Small, T., Complex Polynomials, Cambridge University Press, Cambridge, 2002.
  9. Walsh, J. L., Sur la position des racines des d´eriv´ees d’un polynome, C. R. Acad. Sci. Paris 172 (1921), 662–664.
10.2478/v10062-012-0025-x
- Full text in PDF format

Article 02EN: Estimates of Lp norms for sums of positive functions
11-16

I. R. KAYUMOV


Kazan Federal University,Russia e-mail: ikayumov@ksu.ru

We present new inequalities of Lp norms for sums of positive functions. These inequalities are useful for investigation of convergence of simple partial fractions in Lp(R).
  1. Protasov, V. Yu., Approximation by simple partial fractions and the Hilbert transform, Izv. Math. 73 (2) (2009), 333–349.
  2. Kayumov, I. R., Convergence of simple partial fractions in Lp(R), Sb. Math. 202 (10) (2011), 1493–1504.
  3. Hardy, G. H., Littlewood, J. E., Pólya, G., Inequalities, Cambridge University Press, Cambridge, 1934.
10.2478/v10062-012-0026-9
- Full text in PDF format

Article 03EN: Some results on local fields
17-32

AKRAM LBEKKOURI


Akram Lbekkouri, BP: 10507, Casa-Bandoeng 20002, Casablanca, Morocco e-mail: lbeka11@gmail.com

Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.
  1. Abbes, A., Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (5) (2002), 879–920.
  2. Artin, E., Galois Theory, Univ. of Notre Dame Press, Notre Dame, 1942. [3] Hazewinkel, M., Local class field theory is easy, Adv. Math. 18 (1975), 148–181.
  3. Lbekkouri, A., On the construction of normal wildly ramified over Qp, (p _= 2), Arch. Math. (Basel) 93 (2009), 331–344.
  4. Ribes, L., Zalesskii, P., Profinite Groups, Springer-Verlag, Berlin, 2000.
  5. Rotman, J. J., An Introduction to the Theory of Group, Springer-Verlag, New York, 1995.
  6. Serre, J.-P., Local Fields, Springer-Verlag, New York–Berlin, 1979.
  7. Zariski, O., Samuel, P., Commutative Algebra. Volume II, Springer-Verlag, New York– Heidelberg, 1975.
  8. Zhukov, I. B., On ramification theory in the imperfect residue field case, Preprint No. 98-02, Nottingham Univ., 1998. Proceedings of the conference: Ramification Theory of Arithmetic Schemes (Luminy, 1999) (ed. B. Erez), http://family239.narod.ru/math/publ.htm.
10.2478/v10062-012-0027-8
- Full text in PDF format

Article 04EN: Properties of functions concerned with Carath´eodory functions
33-41

MAMORU NUNOKAWA 1, EMEL YAVUZ DUMAN 2, SHIGEYOSHI OWA 3


1 Emeritus Professor of University of Gunma, Hoshikuki 798-8, Chuou-Ward, Chiba, Chiba 260–0808, Japan e-mail: mamoru nuno@doctor.nifty.jp
2 Department of Mathematics and Computer Science, İstanbul Kültür University 34156 Bakıröy, İstanbul Turkey e-mail: e.yavuz@iku.edu.tr

Let Pn denote the class of analytic functions p(z) of the form p(z) = 1+cnzn + cn+1zn+1 + . . . in the open unit disc U. Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289–305), some interesting properties for p(z) concerned with Carath´eodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradović and S. Owa (Math. Nachr. 140 (1989), 97–102) are shown.
  1. Carath´eodory, C., ¨ Uber den Variabilitatsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann. 64(1907), 95–115.
  2. Jack, I. S., Functions starlike and convex of order α, J. London Math. Soc. 3 (1971), 469–474.
  3. Miller, S. S., Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289–305.
  4. Nunokawa, M., On the Bazilević analytic functions, Sci. Rep. Fac. Edu. Gunma Univ. 21 (1972), 9–13.
  5. Obradović, M., Owa, S., A criterion for starlikeness, Math. Nachr. 140 (1989), 97– 102.
  6. Umezawa, T., Analytic functions convex in one direction, J. Math. Soc. Japan 4 (1952), 194–202.
10.2478/v10062-012-0028-7
- Full text in PDF format

Article 05EN: Strongly gamma-starlike functions of order alpha
43-51

MAMORU NUNOKAWA 1, JANUSZ SOKOŁ 2


1 University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba, 260-0808, Japan, e-mail: mamoru−nuno@doctor.nifty.jp
2 Department of Mathematics, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland, e-mail: jsokol@prz.edu.pl

In this work we consider the class of analytic functions G(α, γ), which is a subset of gamma-starlike functions introduced by Lewandowski, Miller and Złotkiewicz in Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska, Sect. A 28 (1974), 53–58. We discuss the order of strongly starlikeness and the order of strongly convexity in this subclass.
  1. Brannan, D. A., Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. 1 (2) (1969), 431–443.
  2. Lewandowski, Z., Sur l’identit´e de certaines classes de fonctio
  3. Lewandowski, Z., Miller, S., Złotkiewicz, E., Gamma starlike functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 28 (1974), 53–58.
  4. Nunokawa, M., On properties of non-Carath´eodory functions, Proc. Japan Acad. Ser. A 68 (6) (1992), 152–153.
  5. Nunokawa, M., On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A 69 (7) (1993), 234–237.
  6. Robertson, M. S., On the theory of univalent functions, Ann. Math. 37 (1936), 374– 408.
  7. Sokół, J., On sufficient condition to be in a certain subclass of starlike functions defined by subordination, Appl. Math. Comp. 190 (2007), 237–241.
  8. Stankiewicz, J., Quelques probl`emes extr`emaux dans les classes des fonctions α- angulairement `etoil`ees, Ann. Univ. Mariae Curie-Skłodowska Sect. A 20 (1966), 59–75.
  9. Wilken, D. R., Feng, J, A remark on convex and starlike functions, J. London Math. Soc. 21 (2) (1980), 287–290.
10.2478/v10062-012-0029-6
- Full text in PDF format

Article 06EN: An integral operator on the classes S∗(α) and CVH(β)
53-58

NICOLETA ULARU 1, NICOLETA BREAZ 2


1 University of Piteşti, Târgul din Vale Str., No. 1, 110040 Piteşti, Argeş¸Romania, e-mail: nicoletaularu@yahoo.com
2 1 Decembrie 1918 University of Alba Iulia, N. Iorga Str., No. 11–13, 510009 Alba Iulia, Alba, Romania, e-mail: nbreaz@uab.ro

The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order α and from the class CVH(β) and also we estimate the first two coefficients for functions obtained by this operator applied on the class CVH(β).
  1. Acu, M., Owa, S., Convex functions associated with some hyperbola, J. Approx. Theory Appl. 1 (1) (2005), 37–40.
  2. Breaz, N., Breaz, D., Acu, M., Some properties for an integral operator on the CVH(β)- class , IJOPCA 2 (1) (2010), 53–58.
  3. Pescar, V., The univalence of an integral operator, Gen. Math. 19 (4) (2011), 69–74.
  4. Robertson, M. S., Certain classes of starlike functions, Michigan Math. J. 76 (1) (1954), 755–758.
  5. Ularu, N., Convexity properties for an integral operator, Acta Univ. Apulensis Math. Inform. 27 (2011), 115–120.
10.2478/v10062-012-0030-0
- Full text in PDF format

Article 07EN: Remarks on some recent results about polynomials with restricted zeros
59-64

M. A. QAZI


Department of Mathematics, Tuskegee University, Tuskegee, Alabama 36088, U.S.A., e-mail: qazima@aol.co

We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Skłodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question.
  1. Ahuja, A., Dewan, K. K., Hans, S., Inequalities concerning polar derivative of polynomials, Ann. Univ. Mariae Curie-Skłodowska Sect. A 65 (2011), 1–9.
  2. Dewan, K. K., Hans, S., On maximum modulus for the derivative of a polynomial, Ann. Univ. Mariae Curie-Skłodowska Sect. A 63 (2009), 55–62.
  3. Govil, N. K., On the derivative of a polynomial, Proc. Amer. Math. Soc. 41 (1973), 543–546.
  4. Govil, N. K., On a theorem of S. Bernstein, J. Math. Phys. Sci. 14 (1980), 183–187.
  5. Rahman, Q. I., Schmeisser, G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002.
10.2478/v10062-012-0031-z
- Full text in PDF format

Article 08EN: Coefficient bounds for some subclasses of p-valently starlike functions
65-78

C. SELVARAJ 1, O. S. BABU 2, G. MURUGUSUNDARAMOORTHY 3


1 Department of Mathematics, Presidency College (Autonomous), Chennai – 600005, India, e-mail: pamc9439@yahoo.co.in
2 Department of Mathematics, Dr. Ambedkar Govt. Arts College, Chennai – 600039, India, e-mail: osbabu1009@gmail.com
3 School of Advanced Sciences, VIT university, Vellore - 632 014, India, e-mail: gmsmoorthy@yahoo.com

For functions of the form f(z) = zp ∑_(n=1)^∞▒a_(p+n) Z^(p+n) we obtain sharp bounds for some coefficients functionals in certain subclasses of starlike functions. Certain applications of our main results are also given. In particular, Fekete–Szeg¨o-like inequality for classes of functions defined through extended fractional differintegrals are obtained.
  1. Ali, R. M., Ravichandran, V., Seenivasagan, N., Coefficient bounds for p-valent functions, Appl. Math. Comput. 187 (2007), 35–46.
  2. Janowski, W., Some extremal problems for certain families of analytic functions, Bull. Acad. Polon. Sci. S´er. Sci. Math. Astronom. Phys. 21 (1973), 17–25.
  3. Keogh, F. R., Merkes, E. P., A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12.
  4. Ma, W. C., Minda, D., A unified treatment of some special classes of univalent functions, Proceedings of the Conference on Complex Analysis (Tianjin, 1992), Int. Press, Cambridge, MA, 1994, 157–169.
  5. Owa, S., On the distortion theorem. I, Kyungpook Math. J. 18 (1) (1978), 53–59.
  6. Owa, S., Srivastava, H. M., Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 (5) (1987), 1057–1077.
  7. Patel, J., Mishra, A., On certain subclasses of multivalent functions associated with an extended differintegral operator, J. Math. Anal. Appl. 332 (2007), 109–122.
  8. Prokhorov, D. V., Szynal, J., Inverse coefficients for (α, β)-convex functions, Ann. Univ. Mariae Curie-Skłodowska Sect. A 35 (1981), 125–143.
  9. Selvaraj, C., Selvakumaran, K. A., Fekete–Szeg¨o problem for some subclass of analytic functions, Far East J. Math. Sci. (FJMS) 29 (3) (2008), 643–652.
  10. Srivastava, H. M., Mishra, A. K., Das, M. K., The Fekete–Szeg¨o problem for a subclass of close-to-convex functions, Complex Variables Theory Appl. 44 (2) (2001), 145–163.
  11. Srivastava, H. M., Owa, S., An application of the fractional derivative, Math. Japon. 29 (3) (1984), 383–389.
  12. Srivastava, H. M., Owa, S., Univalent Functions, Fractional Calculus and their Applications, Halsted Press/John Wiley & Sons, Chichester–New York, 1989.
10.2478/v10062-012-0032-y
- Full text in PDF format

Volume 66 - 2012

Article 01EN: The vertical prolongation of the projectable connections
1-5

Anna Bednarska

We prove that any first order F2MMm1,m2,n1,n2-natural operatortransforming projectable general connections on an (m1;m2; n1; n2)-dimensional fibred-fibred manifold p = (p; p) : (pY : Y → Y ) -> (pM : M → M) into general connections on the vertical prolongation VY → M of p: Y → M is the restriction of the (rather well-known) vertical prolongation operator V lifting general connections Γ on a fibred manifold Y → M into VΓ (the vertical prolongation of Γ) on VY → M.
  1. Doupovec, M., Mikulski, W. M., On the existence of prolongation of connections, Czechoslovak Math. J., 56 (2006), 1323–1334.
  2. Kol´aˇr, I., Connections on fibered squares, Ann. Univ. Mariae Curie-Skłodowska Sect. A 59 (2005), 67–76.
  3. Kol´aˇr, I., Michor, P. W. and Slov´ak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.
  4. Kol´aˇr, I., Mikulski, W. M., Natural lifting of connections to vertical bundles, The Proceedings of the 19th Winter School “Geometry and Physics” (Srn´ı, 1999). Rend. Circ. Mat. Palermo (2) Suppl. No. 63 (2000), 97–102.
  5. Kurek, J., Mikulski, W. M., On prolongations of projectable connections, Ann. Polon. Math, 101 (2011), no. 3, 237–250.
  6. Mikulski, W. M., The jet prolongations of fibered-fibered manifolds and the flow operator, Publ. Math. Debrecen 59 (2001), no. 3–4, 441–458.
  7. Kol´aˇr, I., Some natural operations with connections, J. Nat. Acad. Math. India 5 (1987), no. 2, 127–141.
10.2478/v10062-012-0001-5
- Full text in SWF DJVU PDF format

Article 02EN: Affine invariants of annuli
7-12

Waldemar Cieślak, Elżbieta Szczygielska

A family of regular annuli is considered. Affine invariants of annuli are introduced.
10.2478/v10062-012-0002-4
- Full text in SWF DJVU PDF format

Article 03EN: On certain general integral operators
13-23

B. A. Frasin

In this paper, we obtain new sufficient conditions for the operators Fα1,α2,...,αn(z) and Gα1,α2,...,αn,β(z) to be univalent in the open unit disc U, where the functions f1,f2,...,fn belong to the classes S*(a; b) and K(a; b). The order of convexity for the operators Fα1,α2,...,αn,β(z) and Gα1,α2,...,αn,β(z) is also determined. Furthermore, and for β=1; we obtain sufficient conditions for the operators Fn(z) and Gn(z) to be in the class K(a; b). Several corollaries and consequences of the main results are also considered.
10.2478/v10062-012-0003-3
- Full text in SWF DJVU PDF format

Article 04EN: Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space
25-39

Michael Gil’

We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
10.2478/v10062-012-0004-2
- Full text in SWF DJVU PDF format

Article 05EN: Cartan connection of transversally Finsler foliation
41-48

Andrzej Miernowski

The purpose of this paper is to define transversal Cartan
10.2478/v10062-012-0005-1
- Full text in SWF DJVU PDF format

Article 06EN: Integral formula for secantoptics and its application
49-62

Witold Mozgawa, Magdalena Skrzypiec

Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieslak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results.
10.2478/v10062-012-0006-0
- Full text in SWF DJVU PDF format

Article 07EN: English: On inclusion relationships of certain subclasses of meromorphic functions involving integral operator
63-73

Ali Muhammad

In this paper, we introduce some subclasses of meromorphic functions in the punctured unit disc. Several inclusion relationships and some other interesting properties of these classes are discussed.
10.2478/v10062-012-0007-z
- Full text in SWF DJVU PDF format

Article 08EN: Boundedness and compactness of weighted composition operators between weighted Bergman spaces
75-81

Elke Wolf

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.
10.2478/v10062-012-0008-y
- Full text in SWF DJVU PDF format

Article 01EN: English: Equality cases for condenser capacity inequalities under symmetrization
1-24

Dimitrios Betsakos, Stamatis Pouliasis


Department of Mathematics Aristotle University of Thessaloniki 54124 Thessaloniki Greece e-mail: betsakos@math.auth.gr, spoulias@math.auth.gr

It is well known that certain transformations decrease the capacity of a condenser. We prove equality statements for the condenser capacity inequalities under symmetrization and polarization without connectivity restrictions on the condenser and without regularity assumptions on the boundary of the condenser.
10.2478/v10062-012-0009-x
- Full text in SWF PDF format

Article 02EN: On a question of T. Sheil-Small regarding valency of harmonic maps
25-29

Daoud Bshouty 1, Abdallah Lyzzaik 2


1 Department of Mathematics, Technion, Haifa, Israel
2 Department of Mathematics, American University of Beirut, Beirut, Lebanon

The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping  from the unit circle into itself ofthe form (eit) = eiᵠ(t); 0 ≤ t ≤2; where ᵠ is a continuously non-decreasing function that satisfies ᵠ (2)-ᵠ (0) = 2N; assume every value finitely many times in the disc?
10.2478/v10062-012-0010-4
- Full text in SWF PDF format

Article 03EN: Classes of meromorphic multivalent functions with Montel’s normalization
31-46

Jacek Dziok


University of Rzeszów, Institute of Mathematics, 35-310 Rzeszów, Poland

In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.
10.2478/v10062-012-0011-3
- Full text in SWF PDF format

Article 04EN: On Perelman’s functional with curvature corrections
47-55

Rami Ahmad El-Nabulsi


College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, China

In recent ten years, there has been much concentration and increased research activities on Hamilton’s Ricci flow evolving on a Riemannian metric and Perelman’s functional. In this paper, we extend Perelman’s functional approach to include logarithmic curvature corrections induced by quantum effects. Many interesting consequences are revealed.
10.2478/v10062-012-0012-2
- Full text in SWF PDF format

Article 05EN: Majorization for certain classes of meromorphic functions defined by integral operator
57-62

S. P. Goyal 1, Pranay Goswami 2


1 Department of Mathematics, University of Rajasthan, Jaipur-302055, India
2 Department of Mathematics, AMITY University Rajasthan, Jaipur-302002, India

Here we investigate a majorization problem involving starlike meromorphic functions of complex order belonging to a certain subclass of meromorphic univalent functions defined by an integral operator introduced recently by Lashin.
10.2478/v10062-012-0013-1
- Full text in SWF PDF format

Article 06EN: Generalization of p-regularity notion and tangent cone description in the singular case
63-79

Wiesław Grzegorczyk 1, Beata Medak 1, Alexey A. Tret’Yakov 1;2;3


1 Department of Mathematics and Physics, Siedlce University of Natural Sciences, and Humanities, ul. 3-go Maja 54, 08-110 Siedlce, Poland
2 System Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland
3 Dorodnicyn Computing Center, Russian Academy of Sciences, Vavilova 40, Moscow, 119991, Russia

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions.
10.2478/v10062-012-0014-0
- Full text in SWF PDF format

Article 07EN: On a result by Clunie and Sheil-Small
81-92

Dariusz Partyka 1;2, Ken-Ichi Sakan 3


1 Faculty of Mathematics and Natural Sciences, The John Paul II Catholic University of Lublin, Al. Racławickie 14, P.O. Box 129, 20-950 Lublin, Poland
2 Institute of Mathematics and Computer Science, The State University of Applied Science in Chełm, ul. Pocztowa 54, 22-100 Chełm, Poland
3 Department of Mathematics, Graduate School of Science, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk D, if F(D) is a convex domain, then the inequality |G(z2)-G(z1)| < |H(z2)- H(z1)| holds for all distinct points z1, z2  D. Here H and G are holomorphic mappings in D determined by F = H + G, up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain  in C and improve it provided F is additionally a quasiconformal mapping in .
10.2478/v10062-012-0015-z
- Full text in SWF PDF format

Article 08EN: Solution of a class of the first kind singular integral equation with multiplicative Cauchy kernel
93-105

Paweł Wójcik, Michail A. Sheshko, Dorota Pylak, Paweł Karczmarek


Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Al. Racławickie 14, 20-950 Lublin, Poland

In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
10.2478/v10062-012-0016-y
- Full text in SWF PDF format

Volume 65 - 2011

Article 01EN: Inequalities concerning polar derivative of polynomials
1-9

Arty Ahuja, K. K. Dewan, Sunil Hans


Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia (Central University), New Delhi-110025, India Abstract

In this paper we obtain certain results for the polar derivative of a polynomial , having all its zeros on which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted zeros.
Polynomials, maximum modulus, inequalities in the complex domain, polar derivative
10.2478/v10062-011-0001-x
- Full text in SWF PDF format

Article 02EN: Lagrangians and Euler morphisms on fibered-fibered frame bundles from projectable-projectable classical linear connections
11-19

Anna Bednarska


Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

We classify all F2Mm1, m2, n1, n2-natural operators Atransforming projectable-projectable torsion-free classical linear connections ∇ on fibered-fibered manifolds Y of dimension (m1,m2, n1, n2) into rth order Lagrangians A(∇) on the fibered-fibered linear frame bundle Lfib-fib(Y) on Y. Moreover, we classify all F2Mm1, m2, n1, n2-natural operators B transforming projectable-projectable torsion-free classical linear connections ∇ on fiberedfibered manifolds Y of dimension (m1, m2, n1, n2) into Euler morphism B(∇) on Lfib-fib(Y. These classifications can be expanded on the kth order fibered-fibered frame bundle Lfib-fib,k(Y) instead of Lfib-fib(Y).

Fibered-fibered manifold, Lagrangian, Euler morphism, natural operator, classical linear connection
10.2478/v10062-011-0002-9
- Full text in SWF PDF format

Article 03EN: On the central limit theorem for some birth and death processes
21-31

Tymoteusz Chojecki


ul. Czeremchowa 12/26, 20-807 Lublin, Poland

Suppose that {Xn, n ≥ 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem converge in law to a normal random variable, as N → +∞. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for which the CLT holds for a class of birth and death chains whose dynamics has no spectral gap, so that Gordin's result cannot be used and the result follows from an application of Kipnis-Varadhan theory.

Central limit theorem, Markov chain, Lamperti's problem, birth and death processes, Kipnis-Varadhan theory, spectral gap
10.2478/v10062-011-0003-8
- Full text in SWF PDF format

Article 04EN: Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution
33-48

Rabha M. El-Ashwah 1, Mohamed K. Aouf 2, S. M. El-Deeb 1


1 Department of Mathematics, Faculty of Science at Damietta, University of Mansoura, New Damietta 34517, Egypt
2 Department of Mathematics, Faculty of Science, University of Mansoura, Mansoura 33516, Egypt

In this paper we introduce and investigate three new subclasses of p-valent analytic functions by using the linear operator Dmλ,p(f * g)(z). The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for (n, θ)-neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.
Analytic, p-valent, (nθ)-neighborhood, inclusion relations
10.2478/v10062-011-0004-7
- Full text in SWF PDF format

Article 05EN: Extended fractional calculus of variations, complexified geodesics and Wong's fractional equations on complex plane and on Lie algebroids
49-67

Rami Ahmad El-Nabulsi 1;2


1 Department of Nuclear Engineering, Cheju National University, Ara-dong 1, Jeju 690-756, South Korea
2 College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112, China

In this work, we communicate the topic of complex Lie algebroids based on the extended fractional calculus of variations in the complex plane. The complexified Euler-Lagrange geodesics and Wong's fractional equations are derived. Many interesting consequences are explored.
Extended fractional calculus, complex plane, complex Lie algebroids
10.2478/v10062-011-0005-6
- Full text in SWF PDF format

Article 06EN: Inequalities and limit theorems for random allocations
69-85

István Fazekas 1, Alexey Chuprunov 2, József Túri 3


1 Faculty of Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary
2 Department of Math. Stat. and Probability, Kazan State University, Universitetskaya 17, 420008 Kazan, Russia
3 Faculty of Mechanical Engineering and Informatics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary Abstract

Random allocations of balls into boxes are considered. Properties of the number of boxes containing a fixed number of balls are studied. A moment inequality is obtained. A merge theorem with Poissonian accompanying laws is proved. It implies an almost sure limit theorem with a mixture of Poissonian laws as limiting distribution. Almost sure versions of the central limit theorem are obtained when the parameters are in the central domain.
Random allocation, moment inequality, merge theorem, almost sure limit theorem
10.2478/v10062-011-0006-5
- Full text in SWF PDF format

Article 07EN: Some framed f-structures on transversally Finsler foliations
87-96

Cristian Ida


Department of Algebra, Geometry and Differential Equations, Transilvania University of Braşov, Braşsov 500091, Str. Iuliu Maniu 50, România

Some problems concerning to Liouville distribution and framed f-structures are studied on the normal bundle of the lifted Finsler foliation to its normal bundle. It is shown that the Liouville distribution of transversally Finsler foliations is an integrable one and some natural framed f(3, ε)-structures of corank 2 exist on the normal bundle of the lifted Finsler foliation.
Transversally Finsler foliation, Liouville distribution, framed f-structures
10.2478/v10062-011-0007-4
- Full text in SWF PDF format

Article 08EN: On the zeros of polynomials and analytic functions
97-108

Roshan Lal 1, Susheel Kumar 2, Sunil Hans 2


1 Department of Mathematics, Government Degree College, Chaubattakhal (Pauri), Uttrakhand 246 162, India
2 Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia (Central University), New Delhi - 110025, India

For a polynomial of degree n, we have obtained some results, which generalize and improve upon the earlier well known results (under certain conditions). A similar result is also obtained for analytic function.
Polynomial, analytic function, zeros
10.2478/v10062-011-0008-3
- Full text in SWF PDF format

Article 01EN: A note on Professor Jan Grzegorz Krzyż
VII-VIII

Eligiusz Złotkiewicz

10.2478/v10062-011-0026-1
- Full text in SWF PDF format

Article 02EN: On Kaluza's sign criterion for reciprocal power series
1-16

Árpád Baricz 1, Jetro Vesti 2, Matti Vuorinen 2


1 Department of Economics, Babeş-Bolyai University, Cluj-Napoca 400591, Romania
2 Department of Mathematics, University of Turku, Turku 20014, Finland

T. Kaluza has given a criterion for the signs of the power series of a function that is the reciprocal of another power series. In this note the sharpness of this condition is explored and various examples in terms of the Gaussian hypergeometric series are given. A criterion for the monotonicity of the quotient of two power series due to M. Biernacki and J. Krzyż is applied.
Power series, log-convexity, hypergeometric functions, trigonometric functions
10.2478/v10062-011-0009-2
- Full text in SWF PDF format

Article 03EN: On a theorem of Haimo regarding concave mappings
17-28

Martin Chuaqui 1, Peter Duren 2, Brad Osgood 3


1 Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
2 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043, U.S.A.
3 Department of Electrical Engineering, Stanford University, Stanford, California 94305, U.S.A. Abstract

A relatively simple proof is given for Haimo's theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo's criterion, which is now shown to be sharp. It is proved that Haimo's functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.
Concave mapping, Schwarzian derivative, Schwarzian norm, Haimo's theorem, univalence, Sturm comparison, asymptotically conformal curve
10.2478/v10062-011-0010-9
- Full text in SWF PDF format

Article 04EN: About a Pólya-Schiffer inequality
29-44

Bodo Dittmar 1, Maren Hantke 2


1 Institut für Analysis, Martin-Luther-Universität, Halle-Wittenberg, D-06099 Halle (Saale), Germany
2 Institut für Analysis und Numerik, Otto-von-Guericke-Universität Magdeburg, D-39016 Magdeburg, Germany

For simply connected planar domains with the maximal conformal radius 1 it was proven in 1954 by G. Pólya and M. Schiffer that for the eigenvalues λ of the fixed membrane for any n the following inequality holds where λ(o) are the eigenvalues of the unit disk. The aim of the paper is to give a sharper version of this inequality and for the sum of all reciprocals to derive formulas which allow in some cases to calculate exactly this sum.
Membrane eigenvalues, sums of reciprocal eigenvalues
10.2478/v10062-011-0011-8
- Full text in SWF PDF format

Article 05EN: On a theorem of Lindelöf
45-51

Vladimir Gutlyanskii 1, Olli Martio 2, Vladimir Ryazanov 1


1 Institute of Applied Mathematics and Mechanics, NAS of Ukraine, ul. Roze Luxemburg 74, 84114, Donetsk, Ukraine
2 Department of Mathematics and Statistics, University of Helsinki, University of Helsinki, P. O. Box 68, Gustaf Hällströmin katu 2b, FIN-00014, Finland

We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.
Lindelöf theorem, infinitesimal geometry, continuous extension to the boundary, differentiability at the boundary, conformal and quaisconformal mappings
10.2478/v10062-011-0012-7
- Full text in SWF PDF format

Article 06EN: Eine Klasse nichtschlichter konformer Abbildungen mit einer schlichten quasikonformen Fortsetzung. II
53-61

Reiner Kühnau


FB Mathematik der Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle/Saale, Deutschland

We study a dual analogue of the class Σ(κ) of hydrodynamically normalized schlicht conformal mappings g(z) of the exterior of the unit circle with a -quasiconformal extension, namely now those (non-schlicht) mappings g(z) for which g(z) has such a quasiconformal extension.
Non-schlicht functions, quasiconformal extension
10.2478/v10062-011-0013-6
- Full text in SWF PDF format

Article 07EN: Structure fractals and para-quaternionic geometry
63-73

Julian Ławrynowicz 1, Massimo Vaccaro 2


1 Institute of Physics, University of Łódź, Pomorska 149/153, PL-90-236 Łódź, Poland
2 Dipartimento dell'Ingegneria di Informazione e Matematica Applicata, Università di Salerno, I-84084 Fisciano (SA), Italy

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of the flower type related to complex and Pauli structures and, in relation to the iteration process pp + 2 ← p + 4 ← …, they have constructed 24-dimensional "bipetals" for p = 9 and 27-dimensional "bisepals" for p = 13. The objects constructed appear to have an interesting property of periodicity related to the gradating function on the fractal diagonal interpreted as the "pistil" and a family of pairs of segments parallel to the diagonal and equidistant from it, interpreted as the "stamens". The first named author, M. Nowak-Kępczyk, and S. Marchiafava (2006, 2009a, b) gave an effective, explicit determination of the periods and expressed them in terms of complex and quaternionic structures, thus showing the quaternionic background of that periodicity. In contrast to earlier results, the fractal bundle flower structure, in particular petals, sepals, pistils, and stamens are not introduced ab initio; they are quoted a posteriori, when they are fully motivated. Physical concepts of dual and conjugate objects as well as of antiparticles led us to extend the periodicity theorem to structure fractals in para-quaternionic formulation, applying some results in this direction by the second named author. The paper is concluded by outlining some applications.
Fractal, quaternion, para-quaternion, Clifford structure, para-quaternionic structure, bilinear form, quadratic form
10.2478/v10062-011-0014-5
- Full text in SWF PDF format

Article 08EN: On Dirichlet type spaces on the unit ball of Cn
75-86

Małgorzata Michalska


Department of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland

In this paper we discuss characterizations of Dirichlet type spaces on the unit ball of Cn obtained by P. Hu and W. Zhang [2], and S. Li [4].
Dirichlet type spaces, holomorphic functions
10.2478/v10062-011-0015-4
- Full text in SWF PDF format

Article 09EN: Möbius invariant Besov spaces on the unit ball of Cn
87-97

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski


Department of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin Poland

We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.
Besov spaces, conformal Möbius transformation
10.2478/v10062-011-0016-3
- Full text in SWF PDF format

Article 10EN: An extension of typically-real functions and associated orthogonal polynomials
99-112

Iwona Naraniecka, Jan Szynal, Anna Tatarczak


Department of Mathematics, University of Higher Education and Innovations, ul. Melgiewska 7-9, 20-209 Lublin, Poland

Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties of obtained orthogonal polynomials.
Typically-real functions, univalent functions, local univalence, univalence, starlikeness, Chebyshev polynomials, orthogonal polynomials
10.2478/v10062-011-0017-2
- Full text in SWF PDF format

Article 11EN: Gauss curvature estimates for minimal graphs
113-120

Maria Nowak, Magdalena Wołoszkiewicz


Department of Mathematics, Maria Curie-Sklodowska University, pl. Marii Curie-Sklodowskiej 1, 20-031 Lublin, Poland

We estimate the Gauss curvature of nonparametric minimal surfaces over the two-slit plane C\((-∞, -1]∪[1, ∞)) at points above the interval (-1, 1).
Harmonic mappings, minimal surfaces, Gauss curvature
10.2478/v10062-011-0018-1
- Full text in SWF PDF format

Article 12EN: On a modification of the Poisson integral operator
121-137

Dariusz Partyka


Faculty of Mathematics and Natural Sciences, The John Paul II Catholic University of Lublin, Al. Raclawickie 14, P.O. Box 129, 20-950 Lublin, Poland

Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue's integrable complex-valued function f on T, Pγ[f] is a complex-valued harmonic function in D and it coincides with the classical Poisson integral of f provided γ is the identity mapping on T. Our considerations are motivated by the problem of spectral values and eigenvalues of a Jordan curve. As an application we establish a relationship between the operator Pγ, the maximal dilatation of a regular quasiconformal Teichmüller extension of γ to D and the smallest positive eigenvalue of γ.
Dirichlet integral, eigenvalue of a Jordan curve, eigenvalue of a quasisymmetric automorphism, extremal quasiconformal mapping, Fourier coefficient, harmonic conjugation operator, harmonic function, Neumann-Poincaré kernel, Poisson integral, quasiconformal mapping, quasisymmetric automorphism, Teichmüller mapping, welding homeomorphism
10.2478/v10062-011-0019-0
- Full text in SWF PDF format

Article 13EN: The Löwner-Kufarev representations for domains with analytic boundaries
139-148

Dmitri Prokhorov


Department of Mathematics and Mechanics, Saratov State University, Saratov 410012, Russia

We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions.
Löwner-Kufarev equation, analytic continuation, univalent polynomials, bounded univalent functions
10.2478/v10062-011-0020-7
- Full text in SWF PDF format

Article 14EN: The Schwarz-Pick theorem and its applications
149-167

M. A. Qazi 1, Q. I. Rahman 2


1 Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, U.S.A.
2 Département de Mathématiques et de Statistique, Université de Montréal, Montréal, Québec H3C 3J7, Canada

Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz-Pick theorem from the geometric theory of functions. We also use the Phragmén-Lindelöf principle, which is of course standard in such situations.
Bernstein's inequality, functions of exponential type in a half-plane, rational functions, Schwarz-Pick theorem
10.2478/v10062-011-0021-6
- Full text in SWF PDF format

Article 15EN: Estimates for polynomials in the unit disk with varying constant terms
169-178

Stephan Ruscheweyh 1, Magdalena Wołoszkiewicz 2


1 Mathematisches Institut, Universitä Würzburg, D-97074 Würzburg
2 Department of Mathematics, Maria Curie-Sklodowska University, pl. Marii Curie-Sklodowskiej 1, 20-031 Lublin, Poland

Let || · || be the uniform norm in the unit disk. We study the quantities Mn (α) := inf (||zP(z) + α|| - α) where the infimum is taken over all polynomials P of degree n - 1 with ||P(z)|| = 1 and α > 0. In a recent paper by Fournier, Letac and Ruscheweyh (Math. Nachrichten 283 (2010), 193-199) it was shown that infα>0Mn (α) = 1/n. We find the exact values of Mn (α) and determine corresponding extremal polynomials. The method applied uses known cases of maximal ranges of polynomials.
Bernstein-type inequalities for complex polynomials, maximal ranges for polynomials
10.2478/v10062-011-0022-5
- Full text in SWF PDF format

Article 16EN: Some gap power series in multidimensional setting
179-190

Józef Siciak


Institute of Mathematics, Jagiellonian University, Lojasiewicza 6, 30-348 Kraków, Poland

We study extensions of classical theorems on gap power series of a complex variable to the multidimensional case.
Plurisubharmonic functions, negligible sets in CN, power series, lacunary power series, multiple power series
10.2478/v10062-011-0023-4
- Full text in SWF PDF format

Article 17EN: Old and new order of linear invariant family of harmonic mappings and the bound for Jacobian
191-202

Magdalena Sobczak-Kneć 1, Viktor V. Starkov 2, Jan Szynal 3


1 Lublin University of Technology, ul. Nadbystrzycka 38D, 20-618 Lublin, Poland
2 Department of Mathematics, University of Petrozavodsk, ul. Lenina 33, 185910 Petrozavodsk, Russia
3 Department of Mathematics, University of Economics and Innovations, ul. Melgiewska 7-9, 20-209 Lublin, Poland

The relation between the Jacobian and the orders of a linear invariant family of locally univalent harmonic mapping in the plane is studied. The new order (called the strong order) of a linear invariant family is defined and the relations between order and strong order are established.
Planar harmonic mappings, order of a linear invariant family, Jacobian
10.2478/v10062-011-0024-3
- Full text in DJVU PDF format

Article 18EN: The Poisson extension of K-quasihomography on the unit circle
203-216

Jan Stankiewicz, Katarzyna Wilczek


Department of Mathematics, Rzeszów University of Technology, ul. W. Pola 2, 35-959 Rzeszów, Poland

In this paper some estimates for the Poisson extension of a K-quasihomography on the unit circle are given.
Poisson extension, quasiconformal, quasisymmetric, quasihomography, cross-ratio
- Full text in SWF PDF format

Volume 64 - 2010

Article 01EN: Subordination and superordination of certain linear operator on meromorphic functions
1-16

M. K. Aouf 1, T. M. Seoudy 2


1 Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516 Egypt
2 Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514 Egypt

Using the methods of differential subordination and superordination, sufficient conditions are determined on the differential linear operator of meromorphic functions in the punctured unit disk to obtain, respectively, the best dominant and the best subordinant. New sandwich-type results are also obtained.
Analytic function, linear operator, Hadamard product, differential subordination, superordination
10.2478/v10062-010-0001-2
- Full text in SWF PDF format

Article 02EN: Inclusion properties of certain subclasses of analytic functions defined by generalized Sălăgean operator
17-26

M. K. Aouf, A. Shamandy, A. O. Mostafa, S. M. Madian


Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516 Egypt

Let A denote the class of analytic functions with the normalization f(0) = f'(0) - 1 = 0 in the open unit disc U = {z : |z| < 1}. Set and define ∞nλ, μ in terms of the Hadamard product . In this paper, we introduce several subclasses of analytic functions defined by means of the operator Inλ, μ A → A, given by . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
Analytic, Hadamard product, starlike, convex
10.2478/v10062-010-0002-1
- Full text in SWF PDF format

Article 03EN: Boehmians of type S and their Fourier transforms
27-43

R. Bhuvaneswari, V. Karunakaran


School of Mathematics, Madurai Kamaraj University, Madurai, India - 625 021

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
Boehmians, spaces of type S, Fourier transform
10.2478/v10062-010-0003-0
- Full text in SWF PDF format

Article 04EN: Horizontal lift of symmetric connections to the bundle of volume forms ν
45-61

Anna Gąsior


Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin Poland

In this paper we present the horizontal lift of a symmetric affine connection with respect to another affine connection to the bundle of volume forms ν and give formulas for its curvature tensor, Ricci tensor and the scalar curvature. Next, we give some properties of the horizontally lifted vector fields and certain infinitesimal transformations. At the end, we consider some substructures of a F(3, 1)-structure on ν.
Horizontal lift, π-conjugate connection, Killing field, infinitesimal transformation, F(3, 1)-structure, FK, FAK, FNK, FQK, FH-structure
- Full text in SWF PDF format

Article 05EN: Harmonic mappings in the exterior of the unit disk
63-73

Jarosław Widomski, Magdalena Gregorczyk


Institute of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin Poland

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.
Harmonic mapping, meromorphic, quasiconformal extension, radius of convexity, radius of univalence
10.2478/v10062-010-0005-y
- Full text in SWF PDF format

Article 06EN: Subclasses of typically real functions determined by some modular inequalities
75-80

Leopold Koczan, Katarzyna Trąbka-Więcław


Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D 20-618 Lublin Poland

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ := {z ∈ C : |z| < 1}, normalized by f(0) = f'(0) - 1 = 0 and such that Im z Im f(z) ≥ 0 for z ∈ Δ. Moreover, let us denote: T(2) := {f ∈ T : f(z) = -f(-z) for z ∈ Δ} and TM, g := {f ∈ T : fMg in Δ}, where M > 1, g ∈ T ∩ S and S consists of all analytic functions, normalized and univalent in Δ.

We investigate classes in which the subordination is replaced with the majorization and the function g is typically real but does not necessarily univalent, i.e. classes {f ∈ T : f &Lt; Mg in Δ}, where M > 1, g ∈ T, which we denote by TM, g. Furthermore, we broaden the class TM, g for the case M ∈ (0, 1) in the following way: TM, g = {f ∈ T : |f(z)| ≥ M|g(z)| for z ∈ Δ}, g ∈ T.

Typically real functions, majorization, subordination
10.2478/v10062-010-0006-x
- Full text in SWF PDF format

Article 07EN: On the order of starlikeness and convexity of complex harmonic functions with a two-parameter coefficient condition
81-91

Agnieszka Sibelska


Departament of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, ul. S. Banacha 22 90-238 Łódź Poland

The article of J. Clunie and T. Sheil-Small [3], published in 1984, intensified the investigations of complex functions harmonic in the unit disc Δ. In particular, many papers about some classes of complex mappings with the coefficient conditions have been published. Consideration of this type was undertaken in the period 1998-2004 by Y. Avci and E. Złotkiewicz [2], A. Ganczar [5], Z. J. Jakubowski, G. Adamczyk, A. Łazińska and A. Sibelska [1], [8], [7], H. Silverman [12] and J. M. Jahangiri [6], among others. This work continues the investigations described in [7]. Our results relate primarily to the order of starlikeness and convexity of functions of the aforementioned classes.
Complex harmonic functions, analytic conditions, convexity of order β, starlikeness of order β
10.2478/v10062-010-0007-9
- Full text in SWF PDF format

Article 08EN: Periodic solutions for second-order Hamiltonian systems with a p-Laplacian
93-113

Xianhua Tang, Xingyong Zhang


School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083 P. R. China

In this paper, by using the least action principle, Sobolev's inequality and Wirtinger's inequality, some existence theorems are obtained for periodic solutions of second-order Hamiltonian systems with a p-Laplacian under subconvex condition, sublinear growth condition and linear growth condition. Our results generalize and improve those in the literature.
Second-order Hamiltonian systems, p-Laplacian, periodic solution, Sobolev's inequality, Wirtinger's inequality, the least action principle
10.2478/v10062-010-0008-8
- Full text in SWF PDF format

Article 01EN: On differential sandwich theorems of analytic functions defined by certain linear operator
1-14

Mohamed K. Aouf 1, Tamer M. Seoudy 2


1 Department of Mathematics, Faculty of Science, Mansoura 35516 Egypt
2 Department of Mathematics, Faculty of Science, Fayoum 63514 Egypt

In this paper, we obtain some applications of first order differential subordination and superordination results involving certain linear operator and other linear operators for certain normalized analytic functions. Some of our results improve and generalize previously known results.
Analytic function, Hadamard product, differential subordination, superordination, linear operator
10.2478/v10062-010-0009-7
- Full text in SWF PDF format

Article 02EN: On the real X-ranks of points of Pn(R) with respect to a real variety X ⊂ Pn
15-19

Edoardo Ballico


Department of Mathematics, University of Trento, 38123 Povo (TN) Italy

Let X ⊂ Pn be an integral and non-degenerate m-dimensional variety defined over R. For any P ∈ Pn(R) the real X-rank r x,R(P) is the minimal cardinality of SX(R) such that P ∈ <S>. Here we extend to the real case an upper bound for the X-rank due to Landsberg and Teitler.
Ranks, real variety, structured rank
10.2478/v10062-010-0010-1
- Full text in SWF PDF format

Article 03EN: On Poncelet's porism
21-28

Waldemar Cieślak 1, Elżbieta Szczygielska 2


1 Zakład Matematyki, Politechnika Lubelska, ul. Nadbystrzycka 40 20-618 Lublin Poland
2 Państwowa Wyższa Szkoła Zawodowa, w Białej Podlaskiej ul. Sidorska 95/97 21-500 Biała Podlaska Poland

We consider circular annuli with Poncelet's porism property. We prove two identities which imply Chapple's, Steiner's and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.
Porism, annulus, bicentric polygon
10.2478/v10062-010-0011-0
- Full text in SWF PDF format

Article 04EN: An extension of the univalence criterion for a family of integral operators
29-35

Erhan Deniz, Halit Orhan


Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey

The main object of the present paper is to extend the univalence condition for a family of integral operators. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.
Integral operator, analytic functions, univalent functions, open unit disk, univalence criterion
10.2478/v10062-010-0012-z
- Full text in SWF PDF format

Article 05EN: Fixed points of periodic mappings in Hilbert spaces
37-48

Víctor Pérez García, Helga Fetter Nathansky


Centro de Investigacion en Matematicas (CIMAT), Apdo. Postal 402 36000, Guanajuato Gto. Mexico

In this paper we give new estimates for the Lipschitz constants of n-periodic mappings in Hilbert spaces, in order to assure the existence of fixed points and retractions on the fixed point set.
Fixed point, retractions, periodic mappings
10.2478/v10062-010-0013-y
- Full text in SWF PDF format

Article 06EN: On subordination for classes of non-Bazilevič type
49-60

Rabha W. Ibrahim 1, Maslina Darus 1, Nikola Tuneski 2


1 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan Malaysia
2 Faculty of Mechanical Engineering, Karpoš II b.b., 1000 Skopje Republic of Macedonia

We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.
Fractional calculus, subordination, non-Bazilevič, function, Jack's lemma
10.2478/v10062-010-0014-x
- Full text in SWF PDF format

Article 07EN: Certain subclasses of starlike functions of complex order involving the Hurwitz—Lerch Zeta function
61-72

G. Murugusundaramoorthy, K. Uma


School of Advanced Sciences, VIT University, Vellore -632014 India

Making use of the Hurwitz—Lerch Zeta function, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients of complex order denoted by TSμ/b (α, β, γ) and obtain coefficient estimates, extreme points, the radii of close to convexity, starlikeness and convexity and neighbourhood results for the class TSμ/b (α, β, γ). In particular, we obtain integral means inequalities for the function f(z) belongs to the class TSμ/b (α, β, γ) in the unit disc.
Univalent, starlike, convex, uniformly convex, uniformly star-like, Hadamard product, integral means, Hurwitz—Lerch Zeta function
10.2478/v10062-010-0015-9
- Full text in SWF PDF format

Article 08EN: On a nonstandard approach to invariant measures for Markov operators
73-80

Andrzej Wiśnicki


Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lubin Poland

We show the existence of invariant measures for Markov-Feller operators defined on completely regular topological spaces which satisfy the classical positivity condition.
Markov operator, invariant measure, nonstandard analysis
10.2478/v10062-010-0016-8
- Full text in SWF PDF format

Volume 63 - 2009

Article 01EN: On certain coefficient bounds for multivalent functions
1-16

Fatma Altuntaş, Muhammet Kamali


Faculty of Sciences, Department of Mathematics, Atatürk University, 25240 Erzurum Turkey

In the present paper, the authors obtain sharp upper bounds for certain coefficient inequalities for linear combination of Mocanu α-convex p-valent functions. Sharp bounds for are derived for multivalent functions.
Analytic functions, starlike functions, convex functions, Mocanu α-convex p-valent functions, subordination, convolution (or Hadamard product)
10.2478/v10062-009-0001-2
- Full text in SWF PDF format

Article 02EN: Differential sandwich theorems for analytic functions defined by Cho—Kwon—Srivastava operator
17-27

Mohamed K. Aouf, Rabha M. El-Ashwah


Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

By making use of Cho-Kwon-Srivastava operator, we obtain some subordinations and superordinations results for certain normalized analytic functions.
Hadamard product, Cho-Kwon-Srivastava operator, subordination, superordination
10.2478/v10062-009-0002-1
- Full text in SWF PDF format

Article 03EN: Inclusion properties of certain subclass of analytic functions defined by multiplier transformations
29-38

Mohamed K. Aouf, Rabha M. El-Ashwah


Math. Dept., Fac. of Sci., Mansoura University, Mansoura 35516, Egypt

Let A denote the class of analytic functions with normalization in the open unit disk . Set and define in terms of the Hadamard product In this paper, we introduce several new subclasses of analytic functions defined by means of the operator . Inclusion properties of these classes and the classes involving the generalized Libera integral operator are also considered.
Subordination, analytic, multiplier transformation, Libera integral operator
10.2478/v10062-009-0003-0
- Full text in SWF PDF format

Article 04EN: On some definition of expectation of random element in metric space
39-48

Artur Bator, Wiesław Zięba


Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland

We are dealing with definition of expectation of random elements taking values in metric space given by I. Molchanov and P. Teran in 2006. The approach presented by the authors is quite general and has some interesting properties. We present two kinds of new results: • conditions under which the metric space is isometric with some real Banach space; • conditions which ensure "random identification" property for random elements and almost sure convergence of asymptotic martingales.
Convex combination, metric space, Banach space, martingale, amart
10.2478/v10062-009-0004-z
- Full text in SWF PDF format

Article 05EN: Almost symplectic structures on the linear frame bundle from linear connection
49-53

Anna Bednarska


Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland

We describe all M fm-natural operators S: QSymp P1 transforming classical linear connections ∇ on m-dimensional manifolds M into almost symplectic structures S(∇) on the linear frame bundle P1M over M.
Classical linear connection, almost symplectic structure, linear frame bundle, natural operator
10.2478/v10062-009-0005-y
- Full text in SWF PDF format

Article 06EN: On maximum modulus for the derivative of a polynomial
55-62

K. K. Dewan, Sunil Hans


Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, (Central University), New Delhi-110025, India

If P(z) is a polynomial of degree n, having all its zeros in the disk then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that

In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type . Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

Polynomials, inequalities, derivatives, zeros
10.2478/v10062-009-0006-x
- Full text in SWF PDF format

Article 07EN: The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences
63-81

Marcin Dudziński


Faculty of Applied Informatics and Mathematics, (Wydział Zastosowań Informatyki i Matematyki), Department of Applied Mathematics (Katedra Zastosowań Matematyki), Warsaw University of Life Sciences (SGGW), ul. Nowoursynowska 159, 02-776 Warszawa, Poland

Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence under certain additional assumptions on {kn} and the covariance function.
Almost sure central limit theorem, knth largest maxima, stationary Gaussian sequences, Normal Comparison Lemma
- Full text in SWF PDF format

Article 08EN: Nonexpansive retractions in Hilbert spaces
83-90

Kazimierz Goebel, Ewa Sędłak


Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Sklodowskiej 1, 20-031 Lublin, Poland

Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.
Hilbert space, convex sets, retractions, nonexpansive mappings
10.2478/v10062-009-0008-8
- Full text in SWF PDF format

Article 09EN: Reduction of absorbing Markov chain
91-107

Mariusz Górajski


The Faculty of Mathematics and Computer Science, University of Łódź, ul. Stefana Banacha 22 90-238 Łódź Poland

In this paper we consider an absorbing Markov chain with finite number of states. We focus especially on random walk on transient states. We present a graph reduction method and prove its validity. Using this method we build algorithms which allow us to determine the distribution of time to absorption, in particular we compute its moments and the probability of absorption. The main idea used in the proofs consists in observing a nondecreasing sequence of stopping times. Random walk on the initial Markov chain observed exclusively in the stopping times τ1, τ2, … is equivalent to some new Markov chain.
Absorbing Markov chain, distribution of time to absorption
10.2478/v10062-009-0009-7
- Full text in SWF PDF format

Article 10EN: Certain family of Durrmeyer type operators
109-115

Vijay Gupta


School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka New Delhi-110078, India

The present paper is a continuation of the earlier work of the author. Here we study the rate of convergence of certain Durrmeyer type operators for function having derivatives of bounded variation.
Bernstein polynomials, Durrmeyer operators, bounded variation, total variation
10.2478/v10062-009-0010-1
- Full text in SWF PDF format

Article 11EN: On univalence of an integral operator
117-132

Szymon Ignaciuk

We consider the problem of univalence of the integral operator (1) . Imposing on functions f(z), g(z) various conditions and making use of a close-to-convexity property of the operator, we establish many suffcient conditions for univalence. Our results extend earlier ones. Some questions remain open.
Univalence, integral operator, close-to-convex
10.2478/v10062-009-0011-0
- Full text in SWF PDF format

Article 12EN: Remarks on best approximation in R-trees
133-138

William A. Kirk 1, Bancha Panyanak 2


1 Department of Mathematics, University of Iowa, Iowa City, IA 52242-1419, USA
2 Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

An R-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. If X is a closed convex subset of an R-tree Y, and if T: X → 2Y is a multivalued mapping, then a point z for which is called a point of best approximation. It is shown here that if T is an ε-semicontinuous mapping whose values are nonempty closed convex subsets of Y, and if T has at least two distinct points of best approximation, then T must have a fixed point. We also obtain a common best approximation theorem for a commuting pair of mappings t: XY and T: X → 2Y where t is single-valued continuous and T is ε-semicontinuous
Best approximation, R-tree, fixed points, semicontinuity
10.2478/v10062-009-0012-z
- Full text in SWF PDF format

Article 13EN: On semi-typically real functions
139-148

Leopold Koczan, Katarzyna Trąbka-Więcław


Department of Applied Mathematics, Lublin University of Technology, ul. Nadbystrzycka 38D, 20-618 Lublin, Poland

Suppose that A is the family of all functions that are analytic in the unit disk Δ and normalized by the condition For a given A ⊂ A let us consider the following classes (subclasses of A): and consists of all univalent members of A. In this paper we investigate the case A = τ, where τ denotes the class of all semi-typically real functions, i.e. . We study relations between these classes. Furthermore, we find for them sets of variability of initial coeffcients, the sets of local univalence and the sets of typical reality.
Typically real functions, sets of variability of coeffcients
10.2478/v10062-009-0013-y
- Full text in SWF PDF format

Article 14EN: Some remarks on strong factorization of tent spaces
149-154

Romi Shamoyan 1, Wen Xu 2


1 Department of Mathematics, Bryansk State University, Russian Federation of Nations
2 Department of Physics and Mathematics, University of Joensuu, P. O. Box 111, FIN-80101 Joensuu, Finland

We provide new assertions on factorization of tent spaces.
Measurable function, tent spaces, factorization
10.2478/v10062-009-0014-x
- Full text in SWF PDF format

Volume 62 - 2008

Article 01EN: Differential sandwich theorems for multivalent functions
1-13

Om P. Ahuja 1, G. Murugusundaramoorthy 2, S. Sivasubramanian 3


1 Department of Mathematics, Kent State University, Burton, Ohio, 44021-9500, USA
2 School of Science and Humanities, VIT University, Vellore-632 014, India
3 Department of Mathematics, Easwari Engineering College, Ramapuram, Chennai-600 089 India

In the present paper, we apply methods based on differential subordinations and superordinations in order to derive several subordination results for multivalent functions involving the Hadamard product.
Analytic functions, convolution product, differential subordinations, differential superordinations, dominant, multivalent functions, subordinant
10.2478/v10062-008-0001-7
- Full text in SWF PDF format

Article 02EN: Differential sandwich theorems for analytic functions defined by some linear operators
15-29

M. K. Aouf, A. O. Mostafa, R. El-Ashwah


Department of Mathematics, Faculty of Science Mansoura University, Mansoura 35516, Egypt

In this investigation, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions. Some of our results improve previous results.
Analytic functions, differential subordination, superordination, sandwich theorems, Dziok-Srivastava operator
10.2478/v10062-008-0002-6
- Full text in SWF PDF format

Article 03EN: Canonical vector valued 1-forms on higher order adapted frame bundles over category of fibered squares
31-36

Anna Bednarska


Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

Let Y be a fibered square of dimension (m1, m2, n1, n2). Let V be a finite dimensional vector space over. We describe all 21,m2,n1,n2 - canonical V -valued 1-form Θ TPrA (Y) → V on the r-th order adapted frame bundle PrA(Y).
Fibered square, projectable-projectable vector field, r-th order adapted frame bundle, canonical 1-forms
10.2478/v10062-008-0003-5
- Full text in SWF PDF format

Article 04EN: Continuity of the quenching time in a semilinear parabolic equation
37-48

Théodore K. Boni 1, Firmin K. N'gohisse 2


1 Institut National Polytechnique, Houphouët-Boigny de Yamoussoukro, BP 1093 Yamoussoukro Côte d'Ivoire
2 Département de Mathmatiques et Informatiques, Université d'Abobo-Adjamé, UFR-SFA, 02 BP 801 Abidjan 02 Côte d'Ivoire

In this paper, we consider the following initial-boundary value problem

where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.

Quenching, nonlinear parabolic equation, numerical quenching time
10.2478/v10062-008-0004-4
- Full text in SWF PDF format

Article 05EN: Circuminscribed polygons in a plane annulus
49-53

Waldemar Cieślak 1, Elżbieta Szczygielska 2


1 Zakład Matematyki, Politechnika Lubelska, ul. Nadbystrzycka 40 20-618 Lublin, Poland
2 Państwowa Wyższa Szkoła Zawodowa, w Białej Podlaskiej ul. Sidorska 95/97 21-500 Biała Podlaska, Poland

Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.
Poncelet's porism, isoptics, parallel curves
10.2478/v10062-008-0005-3
- Full text in SWF PDF format

Article 06EN: Natural affinors on the r-th order adapted frame bundle over fibered-fibered manifolds
55-60

Agnieszka Czarnota


Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

We describe all F2Mm1,m2,n1,n2-natural affinors on the r-th order adapted frame bundle PrAY over (m1,m2, n1, n2)-dimensional fibered-fibered manifolds Y.
Fibered-fibered manifold, r-th order adapted frame bundle, natural affinor
10.2478/v10062-008-0006-2
- Full text in SWF PDF format

Article 07EN: Growth of polynomials whose zeros are outside a circle
61-65

K. K. Dewan, Sunil Hans


Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia (Central University) New Delhi-110025, India

If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that

In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality

Polynomials, inequalities, restricted zeros, growth
10.2478/v10062-008-0007-1
- Full text in SWF PDF format

Article 08EN: Darboux type properties of the paratingent
67-74

Małgorzata Fedor, Joanna Szyszkowska


Department of Real Analysis Faculty of Mathematics and Natural Sciences, The John Paul II Catholic University of Lublin, ul. Konstantynów 1H 20-950 Lublin, Poland

In this paper we consider the Darboux type properties for the paratingent. We review some of the standard facts on the multivalued functions and the paratingent. We prove that the paratingent has always the Darboux property but the property D* holds only when the paratingent is a multivalued function.
Paratingent, Darboux property, multivalued functions
10.2478/v10062-008-0008-0
- Full text in SWF PDF format

Article 09EN: The natural operators lifting vector fields to the bundle of affinors
75-80

Jan Kurek 1, Włodzimierz M. Mikulski 2


1 Institute of Mathematics, Maria Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland
2 Institute of Mathematics, Jagiellonian University, ul. Łojasiewicza 6 30-348 Kraków, Poland

All natural operators TT(TT*) lifting vector fields X from n-dimensional manifolds M to vector fields B(X) on the bundle of affinors T*M are described.
Natural bundles, natural operators
10.2478/v10062-008-0009-z
- Full text in SWF PDF format

Article 10EN: Smith normal form of a matrix of generalized polynomials with rational exponents
81-90

Miroslav Kureš, Ladislav Skula


Institute of Mathematics, Brno University of Technology, Technická 2, 61669 Brno Czech Republic

It is proved that generalized polynomials with rational exponents over a commutative field form an elementary divisor ring; an algorithm for computing the Smith normal form is derived and implemented.
Smith normal form, generalized polynomials with rational exponents
10.2478/v10062-008-0010-6
- Full text in SWF PDF format

Article 11EN: Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself
91-104

Andrzej Michalski


Department of Complex Analysis Faculty of Mathematics and Natural Sciences, The John Paul II Catholic University of Lublin, ul. Konstantynów 1H 20-950 Lublin, Poland

In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.
Harmonic mappings, Poisson integral, quasiconformal mappings
10.2478/v10062-008-0011-5
- Full text in SWF PDF format

Article 12EN: Parallelograms inscribed in a curve having a circle as π/2-isoptic
105-111

Andrzej Miernowski


Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

Jean-Marc Richard observed in [7] that maximal perimeter of a parallelogram inscribed in a given ellipse can be realized by a parallelogram with one vertex at any prescribed point of ellipse. Alain Connes and Don Zagier gave in [4] probably the most elementary proof of this property of ellipse. Another proof can be found in [1]. In this note we prove that closed, convex curves having circles as π/2-isoptics have the similar property.
Convex curve, support function, curvature
10.2478/v10062-008-0012-4
- Full text in SWF PDF format

Article 13EN: Best approximation of coincidence points in metric trees
113-121

Bożena Piątek


Institute of Mathematics, Silesian University of Technology, ul. Kaszubska 23 44-100 Gliwice, Poland

In this work we present results on fixed points, pairs of coincidence points and best approximation for ε-semicontinuous mappings in metric trees. It is a generalization of the similar properties of upper and almost lower semicontinuous mappings.
Metric tree, semicontinuity, fixed points, coincidence points
10.2478/v10062-008-0013-3
- Full text in SWF PDF format

Article 14EN: Uniqueness problem of meromorphic mappings with few targets
123-142

Si Duc Quang, Tran Van Tan


Department of Mathematics, Hanoi National University of Education, 136-Xuan Thuy street, Cau Giay, Hanoi Vietnam

In this paper, using techniques of value distribution theory, we give some uniqueness theorems for meromorphic mappings of Cm into CPn.
Meromorphic mappings, value distribution theory, uniqueness problem
10.2478/v10062-008-0014-2
- Full text in SWF PDF format

Article 15EN: Properties of harmonic conjugates
143-147

Paweł Sobolewski


Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.
Hardy and Littlewood theorem, harmonic conjugate, ap space
10.2478/v10062-008-0015-1
- Full text in SWF PDF format

Article 16EN: Central limit theorem for an additive functional of a Markov process, stable in the Wesserstein metric
149-159

Anna Walczuk


Institute of Mathematics, M. Curie-Skłodowska University, pl. Marii Curie-Skłodowskiej 1 20-031 Lublin, Poland

We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.
Markov process, invariant measure, central limit theorem
10.2478/v10062-008-0016-0
- Full text in SWF PDF format

Volume 61 - 2007

Article 01EN: On pseudo projectively flat LP-Sasakian manifold with a coefficient α
1-8

C. S. Bagewadi, D. G. Prakasha, Venkatesha

Recently, the notion of Lorentzian almost paracontact manifolds with a coefficient α has been introduced and studied by De et al. [1]. In the present paper we investigate pseudo projectively flat LP-Sasakian manifold with a coefficient α.
- Full text in SWF PDF format

Article 02EN: On convexity of the space of random elements
9-14

Artur Bator, Wiesław Zięba

In the space of random elements taking values in a metric space convex in the sense of Doss we may define expected value (see [2]). In this paper we show that the space of random elements with a proper metric is also convex in the sense of Doss if the space of values is convex in the sense of Doss.
- Full text in SWF PDF format

Article 03EN: Some geometric constructions of second order connections
15-22

Miroslav Doupovec, Włodzimierz M. Mikulski

We determine all natural operators A transforming pairs (Θ,nabla) of second order semiholonomic connections Θ: YJ2Y and projectable torsion free classical linear connections nabla on Y into second order semiholonomic connections A(Θ,nabla): YJ2Y.
- Full text in SWF PDF format

Article 04EN: On the theorem of regularity of decrease for universal linearly invariant families of functions
23-38

Ekaterina G. Ganenkova

This article includes results connected with the theorem of regularity of decrease for linearly invariant families Uα of analytic functions in the unit disk. In particular the question about a cardinality of the set of directions of intensive decrease for any function from Uα is considered.
- Full text in SWF PDF format

Article 05EN: Univalent anti-analytic perturbations of convex analytic mappings in the unit disc
39-49

Dominika Klimek-Smęt, Andrzej Michalski

Let SH be the class of normalized univalent harmonic mappings in the unit disc. We introduce subclasses of SH, by choosing only these functions whose analytic parts are convex functions. For such mappings we establish coefficient, growth and distortion estimates. We also give solutions to covering problems. Obtained results are different from those, which are known or conjectured in the full class SH.
- Full text in SWF PDF format

Article 06EN: Diffusion approximation for a G/G/1 EDF queue with unbounded lead times
51-90

Łukasz Kruk

We present a heavy traffic analysis for a G/G/1 queue in which customers have unbounded random deadlines correlated with their service times. The customers are processed according to the earliest-deadline-first (EDF) queue discipline. At any time, the customers have a lead time, the time until their deadline lapses. We model the evolution of these lead times as a random measure on the real line. Under suitable scaling, it is proved that the measure-valued lead-time process converges to a deterministic function of the workload process. This work is a generalization of Doytchinov et al. [6], which developed these results for the case of bounded deadlines independent of the service times. Another generalization of the latter results, covering the case of long range dependence, is also discussed.
- Full text in SWF PDF format

Article 07EN: Generalized Weil functors on affine bundles
91-99

Jan Kurek, Włodzimierz M. Mikulski

We extend the construction by A. Weil onto affine bundles, and prove that all product preserving gauge bundle functors on affine bundles can be obtained by this extended construction.
- Full text in SWF PDF format

Article 08EN: Second order nonholonomic connections from second order nonholonomic ones
101-106

Jan Kurek, Włodzimierz M. Mikulski

We describe all FMm,n-natural operators A: J˜2 rightsquigarrow J˜2 transforming second order nonholonomic connections Θ: YJ˜2 Y on fibred manifolds Y → M into second order nonholonomic connections A(Θ): YJ˜2 Y on Y → M.
- Full text in SWF PDF format

Article 09EN: Sums of holomorphic selfmaps of the unit disk
107-115

Raymond Mortini, Rudolf Rupp

We derive for p > 0 the best constants cp for which whenever |z| ≤ 1. We also determine for 0 ≤ p ≤ 1 all complex numbers c for which the functions are selfmaps of the closed unit disk.
- Full text in SWF PDF format

Article 10EN: Differential sandwich theorems for analytic functions defined by Hadamard product
117-127

G. Murugusundaramoorthy, N. Magesh

In the present investigation, we obtain some subordination and superordination results involving Hadamard product for certain normalized analytic functions in the open unit disk. Our results extend corresponding previously known results.
- Full text in SWF PDF format

Article 11EN: Koebe domains for certain subclasses of starlike functions
129-135

Magdalena Sobczak-Kneć

The Koebe domain's problem in the class of starlike functions with real coefficients was considered by M. T. McGregor [3]. In this paper we determined the Koebe domain for the class of starlike functions with real coefficients and the fixed second coefficient.
- Full text in SWF PDF format

Article 12EN: Inequalities for Bergman spaces
137-143

Paweł Sobolewski

In this paper we prove an inequality for weighted Bergman spaces Aαp, 0 < p < ∞, -1 < α < ∞, that corresponds to Hardy-Littlewood inequality for Hardy spaces. We give also a necessary and sufficient condition for an analytic function f in D to belong to Aαp.
- Full text in SWF PDF format

Article 13EN: On the Ehresmann prolongation
145-153

Petr Vašík

We determine all natural operators transforming general connections Γ: YJ1Y into second order semiholonomic connections Σ: YJ2Y.
- Full text in SWF PDF format

Volume 60 - 2006

Article 01EN: Optimal investment and consumption in the presence of default on a financial market driven by a Lévy noise
1-15

Łukasz Delong

In this paper we investigate a problem of optimal investment and consumption. We consider a financial market consisting of a risk-free asset with a deterministic force of interest and a risky asset whose price is driven by a time-inhomogeneous Lévy process. We also take into account a possibility of default, which is an unpredictable event of exiting a financial market, and we model a default intensity as a diffusion process. The classical verification theorem for the Hamilton-Jacobi-Bellman equation is proved and explicit results are derived for HARA utility functions.
- Full text in SWF PDF format

Article 02EN: Curvatures for horizontal lift of a Riemannian metric
17-21

Anna Gąsior

In this paper we give formulas for coefficients of linear connection and basic curvatures of the bundle of volume forms with the horizontal lift of metric.
- Full text in SWF PDF format

Article 03EN: Covering domains for the class of typically real odd functions
23-30

Leopold Koczan, Paweł Zaprawa

A set f  T(2) f(D) is called the covering domain for the class T(2) of typically real odd functions over some fixed set D. This set is denoted by LT(2)(D). We find sets LT(2)r) and LT(2)(H), where Δr  = {z  C:|z| < r}, r  (0,1) and H = {z  Δ: |1+z22|z|} is one of the domains of univalence for T(2).
- Full text in SWF PDF format

Article 04EN: On a convex class of univalent functions
31-38

Urszula Korzybska, Karol Kowalczyk, Paweł Wójcik

For some M > 0 the classes Qn(M) of all functions z  f(z) =  z + Σj=n+1ajzj analytic on the open unit disk Δ, and such that |f''| ≤ M on Δ, consist only of univalent starlike or convex functions. In the article we get some sharp results in the classes Qn(M), that improve Theorem 5.2f.1 and Corollary 5.5a.1 from the monograph [2] of S. S. Miller and P. T. Mocanu. Applying our results we construct some not trivial examples of univalent starlike or convex functions.
- Full text in SWF PDF format

Article 05EN: Tensor fields on LM induced by tensor fields on M by means of connections on M
39-42

Jan Kurek, Włodzimierz M. Mikulski

We describe all natural operators A transforming a classical linear connection on an m-dimensional manifolds M and a tensor field t of type (r,s) on M into a tensor field A(,t) of type (p,q) on the frame bundle LM over M.
- Full text in SWF PDF format

Article 06EN: Harmonic univalent functions convex in orthogonal directions
43-56

Andrzej Michalski

Many extremal problems in the classes SH and SH0 of normalized univalent harmonic mappings in the unit disk such as coefficient estimates are still opened. However, most of these estimates are conjectured and have been proved for over twenty years in some subclasses of typically real functions, starlike functions, close-to-convex functions, or functions convex in one direction, etc. On the other hand, there is, probably most known and best examined, the subclass of convex functions, in which estimates are completely different from those written above. We introduce new subclasses, by the geometric condition of convexity in two orthogonal directions, in particular, directions of the axis and establish some estimates for them. Obtained results are settled between those proved for convex functions and conjectured in the full classes.
- Full text in SWF PDF format

Article 07EN: A note on transversally Finsler foliations
57-64

Andrzej Miernowski

In the paper [5] a definition of transversally Finsler foliation was given. In this paper we prove a theorem which gives an alternative description of such foliations similar to the case of Riemannian ones. In our considerations transversal cone plays important role. This is a Finsler counterpart of the subspace orthogonal to the leaves.
- Full text in SWF PDF format

Article 08EN: On homogeneous distributions
65-73

Andrzej Miernowski, Witold Rzymowski

Any homogeneous function is determined by its values on the unit sphere. We shall prove that an analogous fact is true for homogeneous distributions.
- Full text in SWF PDF format

Article 09EN: On certain subclasses of multivalent functions involving Cho-Kwon-Srivastava operator
75-86

Jagannath Patel

By making use of the method of differential subordination, we investigate inclusion relationships among certain subclasses of analytic and p-valent functions, which are defined here by means of Cho-Kwon-Srivastava operator Ipλ(a,c). The integral preserving properties in connection with this operator are also studied.
- Full text in SWF PDF format

Volume 59 - 2005

Article 01EN: Local Ramsey numbers for linear forests
1-7

Halina Bielak

Let L be a disjoint union of nontrivial paths. Such a graph we call a linear forest. We study the relation between the 2-local Ramsey number R2-loc(L) and the Ramsey number R(L), where L is a linear forest.

L will be called an (n,j)-linear forest if L has n vertices and j maximal paths having an odd number of vertices. If L is an (n,j)-linear forest, then R2-loc(L) = (3n-j)/2 + |j/2| - 1.

- Full text in SWF PDF format

Article 02EN: On selections of the metric projection and best proximity pairs in hyperconvex spaces
9-17

Rafa Espínola

In this work we present new results on nonexpansive retractions and best proximity pairs in hyperconvex metric spaces. We sharpen the main results of R. Espínola et al. in [3] (Nonexpansive retracts in hyperconvex spaces, J. Math. Anal. Appl. 251 (2000), 557-570) on existence of nonexpansive selections of the metric projection. More precisely we characterize those subsets of a hyperconvex metric space with the property that the metric projection onto them admits a nonexpansive selection as a subclass of sets introduced in [3]. This is a rather exceptional property with a lot of applications in approximation theory, in particular we apply it to answer in the positive the main question posed by Kirk et al. in [5] (Proximinal retracts and best proximity pair theorems, Num. Funct. Anal. Opt. 24 (2003), 851-862).
- Full text in SWF PDF format

Article 03EN: Another proof of the existence of fixed points of rotative nonexpansive mappings
19-26

Jarosław Górnicki

We give a new elementary proof that the condition of rotativeness assures in all Banach spaces, the existence of fixed points of nonexpansive mappings, even without weak compactness, or another special geometric structure.
- Full text in SWF PDF format

Article 04EN: On some classes of functions of Robertson type
27-42

Zbigniew J. Jakubowski, Agnieszka Włodarczyk

Let Δ be the unit disc |z| < 1 and let G(A,B), -1 < A ≤ 1, -A < B ≤ 1 be the class of functions of the form g(z) = 1 Σn=1dnzn, holomorphic and nonvanishing in Δ and such that Re {2zg'(z)/g(z) + (1+Az)/(1-Bz)} > 0 in Δ. It is known that the class G G(1,1) was introduced by M. S. Robertson. A. Lyzzaik has proved the Robertson conjecture on geometric properties of functions  G, g ≠ 1.

In this paper we will investigate the properties of functions of the class G(A,B). In particular when A = B = 1, we will obtain corresponding results of the class G.

- Full text in SWF PDF format

Article 05EN: A nonstandard proof of a generalized demiclosedness principle
43-50

Wiesława Kaczor

Let X be a uniformly convex Banach space, C a nonempty, closed and convex subset of X and let T : C → X be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we present a nonstandard proof of a demiclosedness principle for such T.
- Full text in SWF PDF format

Article 06EN: On covering problems in the class of typically real functions
51-65

Leopold Koczan, Paweł Zaprawa

Let A be a class of analytic functions on the unit disk Δ. In this article we extend the concept of the Koebe set and the covering set for the class A. Namely, for a given D  Δ the plane sets of the form

we define to be the Koebe set and the covering set for the class A over the set D. For any A and D = Δ we get the usual notion of Koebe and covering sets. In the case A = T, the normalized class of typically real functions, we describe the Koebe domain and the covering domain over disks {z: |z| < r}  Δ and over the lens-shaped domain H = {z: |z+i| < √2}∩{z: |z-i| < √2}.
- Full text in SWF PDF format

Article 07EN: Connections on fibered squares
67-76

Ivan Kolár

We clarify that the theory of projectable natural bundles over fibered manifolds is essentially related with the idea of fibered square. We deduce the basic properties of the geometrically most interesting kinds of fibered squares and of the corresponding connections. Special attention is paid to linear square connections of order (q,s,r).
- Full text in SWF PDF format

Article 08EN: The natural transformations TT(r),a → TT(r),a
77-84

Jan Kurek, Włodzimierz M. Mikulski

For integers r ≥ 1 and n ≥ 2 and a real number a < 0 all natural endomorphisms of the tangent bundle TT(r),a of generalized higher order tangent bundle T(r),a over n-manifolds are completely described.
- Full text in SWF PDF format

Article 09EN: On the perfectness of groups of diffeomorphisms with no restriction on support
85-96

Jacek Lech, Tomasz Rybicki

It is well known that the compactly supported identity component of the group of all Cr-diffeomorphisms of a smooth manifold is perfect and simple provided 1 ≤ r ≤ ∞, r ≠ n+1, where n is the dimension of the manifold. Several generalizations for the automorphism groups of geometric structures are known. The problem of the perfectness of analogous groups with no restriction on support is studied. By making use of deformation principles we investigate under what conditions diffeomorphism groups are perfect provided so are their compactly supported subgroups.
- Full text in SWF PDF format

Article 10EN: Types of conditional convergence
97-105

Wioletta Nowak, Wiesław Zięba

The aim of this paper is to investigate relations between different types of conditional convergence. Results presented in this paper generalize theorems obtained by P. Fernandez [2] and A. R. Padmanabhan [5].
- Full text in SWF PDF format

Article 11EN: Convergent infinite products and the minimization of convex functions
107-117

Simeon Reich, Alexander J. Zaslavski

We consider a metric space of sequences of uniformly continuous mappings, acting on a bounded, closed and convex subset of a Banach space, which share a common convex and lower semicontinuous Lyapunov function f. We show that for a generic sequence taken from this space, the corresponding infinite product tends to the unique point where f attains its minimum.
- Full text in SWF PDF format

Article 12EN: Isoptics of open rosettes
119-128

Dominik Szałkowski

In this paper we introduce the notion of an open rosette and its isoptics and prove some theorems such as the sine theorem and its inverse in this framework.
- Full text in SWF PDF format

Article 13EN: On estimating the coefficient product A1A2A3 for real bounded non-vanishing univalent functions
129-139

Olli Tammi

The class of the title is sufficiently limited for allowing certain estimations for combinations of the three first coefficients A1, A2 and A3. The negative sign of A2 implies complications which, however, in the present treatment will be governed, when estimating the product A1A2A3.
- Full text in SWF PDF format

Article 14EN: An example of a nonexpansive mapping which is not 1-ball-contractive
141-146

Andrzej Wiśnicki

We give an example of an isometry defined on a convex weakly compact set which is not 1-ball-contractive. This gives an answer to an open question, implicitly included in Petryshyn (1975), and stated explicitly in Domínguez Benavides and Lorenzo Ramírez (2003, 2004). A fixed point theorem for multivalued contractions is also given.
- Full text in SWF PDF format

Volume 58 - 2004

Article 01EN: Luecking's condition for zeros of analytic functions
1-15

Oscar Blasco, Artur Kukuryka, Maria Nowak

Let A(σ) denote the class of functions f analytic in the unit disk D and such that |f(z)| ≤ Cσ(|z|)+C1, where C, C1 are some positive constants and σ is a nonnegative, nondecreasing function on [0,1). We characterize zero-sets of  f  A(σ) in terms of a subharmonic function introduced by D. Luecking in [7]. Using this characterization we obtain new necessary conditions for A(σ) zero-sets provided log σ satisfies the Dini condition 1/(1-r) ∫01log σ(t)dt  ≤ Clog σ(r). This generalizes the known results obtained, e.g., in [4] and [1].
- Full text in SWF PDF format

Article 02EN: Equipower curves
17-25

Waldemar Cieślak, Robert Stępnicki

In this paper we consider the family of equipower curves. It is proved that each equipower oval has 4n+2 vertices (n ≥ 1) and an example of an equipower oval with exactly six vertices is given. Moreover, it is shown that two vertices lie at ends of one equipower chord. The last sections are devoted to Crofton-type integral formula and estimations of the area and the length of an equipower curve.
- Full text in SWF PDF format

Article 03EN: Ishikawa iterative processes with errors for approximations of zeros of strongly accretive operator equations
27-36

Ljubomir B. Ćirić, Jeong Sheok Ume

In this paper we consider the strong convergence of the sequence of the Ishikawa iterative process with errors to fixed points and solutions of quasi-strongly accretive and quasi-strongly pseudo-contractive operator equations in Banach spaces. Considered error terms are not necessarily summable. Our main results improve and extend the corresponding results recently obtained by Chidume [1], [2], Deng [4], [5], Deng and Ding [6], Liu [8], Xu [11] and Zhou and Jia [12].
- Full text in SWF PDF format

Article 04EN: Asymptotic centers and fixed points for multivalued nonexpansive mappings
37-45

T. Domínguez Benavides, P. Lorenzo

Let X be a nearly uniformly convex Banach space, C a convex closed bounded subset of X and T : C → 2C a multivalued nonexpansive mapping with convex compact values. We prove that T has a fixed point. This result improves former results in [4] and solves an open problem appearing in [17].
- Full text in SWF PDF format

Article 05EN: Natural affinors on time-dependent higher order cotangent bundles
47-58

Štepán Dopita

We study natural affinors on time-dependent natural bundles. Then we determine all natural affinors on the time-dependent higher order cotangent bundle T r*M×R.
- Full text in SWF PDF format

Article 06EN: A note on mappings with nonexpansive square
59-67

Kazimierz Goebel, Wataru Takahashi

Let C be a bounded, closed and convex subset of a Banach space X. We present here some observations on the existence of fixed points for lipschitzian mappings T : C → C having nonexpansive square T 2. We list some problems connected with this class of mappings.
- Full text in SWF PDF format

Article 07EN: Weak and strong convergence of an implicit iterative process for a countable family of nonexpansive mappings in Banach spaces
69-78

Misako Kikkawa, Wataru Takahashi

In this paper, we introduce an implicit sequence for an infinite family of nonexpansive mappings in a uniformly convex Banach space and prove weak and strong convergence theorems for finding a common fixed point of the mappings.
- Full text in SWF PDF format

Article 08EN: Koeffizientenbedingungen vom Grunskyschen Typ und Fredholmsche Eigenwerte
79-87

Reiner Kühnau

We give some remarks and supplements to an important new paper of D. Partyka concerning inequalities of Grunsky type for quasiconformal mappings.
- Full text in SWF PDF format

Article 09EN: Some natural operators in linear vector fields
89-97

Jan Kurek, Włodzimierz M. Mikulski

The higher order tangent bundles of vector bundles are a modification of the usual dual to jets of functions, restricted to those linear along the fibres. The paper shows, roughly speaking, that these bundles are more rigid than their full version.
- Full text in SWF PDF format

Article 10EN: Some remarks about the Goebel-Kirk-Thele mapping
99-116

Enrique Llorens-Fuster

Directly inspired by the well-known construction of a nonlinear self-mapping of the unit ball of the Hilbert space l2 due to K. Goebel and W. A. Kirk, we introduce a new class of uniformly lipschitzian fixed point free mappings.
- Full text in SWF PDF format

Article 11EN: Polynomial approximation of outer functions
117-123

A. Swaminathan

We are interested in finding the polynomial approximants which retain the zero free property of a given analytic function in the unit disk. We show using convolution methods that the classical Cesáro means of order α, as an approximant, retains the zero free property of the derivatives of bounded convex functions in the unit disk. A cone-like conditions is also derived. These results generalizes the earlier results obtained in [1]. We extend this result for other source functions and suitable polynomial approximants.
- Full text in SWF PDF format

Volume 57 - 2003

Article 01EN: Adam Bielecki (1910-2003)
1-10

Jan Kisyński, Jan Krzyż

- Full text in SWF PDF format

Article 02EN: Note on random partitions of the segment
11-22

Milena Bieniek, Dominik Szynal

Let (Xn) be a sequence of independent random variables uniformly distributed on the interval [0,1]. Rn stands for the diameter of the partition of [0,1] by the random points X1, X2, ..., Xn-1. It was shown by R. Jajte that the sequence (nRn / log n) converges to 1 in probability. We prove the convergence in p-th mean, p > 0, of the sequence (nRn / log n) to 1. We are also interested in the rate of convergence in probability of this sequence. Almost sure convergence of (nRn / log n) to 1 is also obtained.
- Full text in SWF PDF format

Article 03EN: A structure of common fixed point sets of commuting holomorphic mappings in finite powers domains
23-33

Monika Budzyńska, Tadeusz Kuczumow

In this paper we consider bounded convex domains D in complex reflexive Banach spaces which are locally uniformly linearly convex in the Kobayashi distance kD. We show that nonempty common fixed point sets of commuting holomorphic mappings in finite powers of these kind of domains are holomorphic retracts.
- Full text in SWF PDF format

Article 04EN: Subordination chains and Loewner differential equations in several complex variables
35-43

Paula Curt, Gabriela Kohr

Let B be the unit ball of Cn with respect to the Euclidean norm and f(z,t) be a Loewner chain. In this paper we study certain properties of f(z,t) and we obtain a sufficient condition for the transition mapping associated to f(z,t) to satisfy the Loewner differential equation.
- Full text in SWF PDF format

Article 05EN: Universal linearity invariant families and Bloch functions in the unit ball
45-58

Janusz Godula, Victor Starkov

In this note we consider universal linearly invariant families of mappings defined in the unit ball. We give a connection of such families with Bloch functions, as well as with Bloch mappings.
- Full text in SWF PDF format

Article 06EN: Liftings of horizontal 1-forms to some vector bundle functors on fibered fibered manifolds
59-68

Jan Kurek, Włodzimierz M. Mikulski

Let F : fibered fibered
manifolds → vector bundle be a vector bundle functor on fibered fibered manifolds. We classify all natural operators

formula I

transforming fibered fibered manifolds-projectable vector fields on Y to functions on the dual bundle (FY)* for any (m1, m2, n1, n2)-dimensional fibered fibered manifold Y. Next, under some assumption on F we study natural operators

formula II

lifting fibered fibered manifolds-horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators

formula II

for a particular vector bundle functor F on fibered fibered manifolds.

- Full text in SWF PDF format

Article 07EN: Horizontal lifts of tensor fields to the bundle of volume forms
-

Andrzej Miernowski, Witold Mozgawa

Dhooghe in [Dho] has given the definition and basic properties of a horizontal lift of a vector field to the bundle of volume forms in order to investigate the Thomas connection from the point of view of projective connection. In this paper we present a systematic approach to the horizontal lift of tensor fields to the bundle of volume forms of basic types of tensors with respect to a symmetric linear connection.
- Full text in SWF PDF format

Article 08EN: Plane convex sets via distributions
77-84

Piotr Pikuta, Witold Rzymowski

We will establish the correspondence between convex compact subsets of R2 and 2π-periodic distributions in R. We also give the necessary and sufficient condition for the positively homogeneous extension u˜ : Rn  → R of u : S n-1 → R to be a convex function.
- Full text in SWF PDF format

Article 09EN: Convoluting to a challenge function
85-93

Herb Silverman, Evelyn M. Silvia

Let A denote the class of functions f that are analytic in Δ = {z : |z| < 1} and normalized by f(0) f'(0) − 1 = 0. The subclasses of A consisting of functions that are univalent in Δ, starlike with respect to the origin, and convex will be denoted by S, S* and K, respectively. In this paper, we investigate conditions under which f  S* has a starlike inverse; i.e., a g  S* for which the convolution f  * g z / (1-z). We also determine conditions under which a fixed h  K can be expressed as h = f  * g where f and g are in S* (or S).
- Full text in SWF PDF format

Article 10EN: On upper semicontinuity of geometric difference of multifunctions
95-97

Joanna Szyszkowska

The short proof of upper semicontinuity of geometric difference of multifunctions is given.
- Full text in SWF PDF format

Article 11EN: On zeros of functions in Bergman and Bloch spaces
99-108

Piotr Waniurski

We generalize some necessary conditions for zero sets of A p functions and Bloch functions obtained in [H] and [GNW], respectively.
- Full text in SWF PDF format

Article 12EN: On a functional equation
109-112

Wojciech Zygmunt

φ(φ(x)) = 2φ(x) - x + p

is studied.

- Full text in SWF PDF format

Volume 56 - 2002

Article 01EN: Almost sure functional limit theorems
1-18

István Fazekas, Zdzisław Rychlik

A general almost sure limit theorem is presented. Then it is applied to obtain almost sure versions of some functional (central) limit theorems.
- Full text in SWF PDF format

Article 02EN: On the modulus of continuity for starlike mappings
19-30

Dieter Gaier, Reiner Kühnau

For a conformal mapping of the unit disk onto a starlike domain with boundary in a given annulus we derive an estimate for the modulus of continuity of the boundary correspondence function. The result is in some sense asymptotically sharp.
- Full text in SWF PDF format

Article 03EN: On the boundary behaviour of functions of several complex variables
31-45

Janusz Godula, Victor Starkov

In this paper we study the boundary behaviour of holomorphic functions defined in either the unit ball, or in the unit polydisk.
- Full text in SWF PDF format

Article 04EN: On the stochastic convergence of conditional expectations of some random sequences
47-52

Krzysztof Kaniowski

Let (Ω, F, P) be a non-atomic probability space and (Xn) be a sequence of integrable random variables. We shall indicate several conditions under which the following conclusion holds: for any random variable Y there exists a sequence (An) of σ-fields such that E(Xn|An)  → Y in probability, for n → ∞.
- Full text in SWF PDF format

Article 05EN: Bemerkung zur quasikonformen Fortsetzung
53-55

Reiner Kühnau

An elementary proof of a theorem of T. Sugawa about quasiconformal extendibility is given.
- Full text in SWF PDF format

Article 06EN: The natural affinors on dual r-jet prolongations of bundles of 2-forms
57-64

Włodzimierz M. Mikulski

Let J r2T*)M be the r-jet prolongation of Λ2T*M of an n-dimensional manifold M. For natural numbers r and n ≥ 3 all natural affinors on (J r2T*)M)* are the constant multiples of the identity affinor only.
- Full text in SWF PDF format

Article 07EN: Constants and symmetries in Banach spaces
65-76

Pier Luigi Papini

In this paper we indicate some connections between some properties of normed spaces and the values of some parameters. We also point out the role of "symmetric" points in minimizing or maximizing quantities involving the numbers ||x - y||, ||x + y||, x and y being on the unit sphere of the space: in fact, the role of these "symmetries" has been sometimes overlooked.
- Full text in SWF PDF format

Article 08EN: On the construction of a stable sequence with given density
77-84

Paul Raynaud De Fitte, Wiesław Zięba

The notion of a stable sequence of events generalizes the notion of mixing sequence and was introduced by A. Rényi. A sequence of random elements X n is said to be stable if for every B   A with P(B) > 0 there exists a probability measure μB on (SB) such that limn→∞P([Xn   A]|B) = μB(A) for every  A with μB(δA= 0. Given a density function, the aim of this note is to give a martingale construction of a stable sequence of random elements having the given density function. The problem was solved in the special case Ω = <0,1> by the second named author and S. Gutkowska.
- Full text in SWF PDF format

Article 09EN: Efficient data-parallel algorithms for computing trigonometric sums
85-96

Przemysław Stpiczyński

In this paper new parallel versions of Goertzel and Reinsch algorithms for calculating trigonometric sums are introduced. To achieve portability, the parallel algorithms have been implemented in High Performance Fortran and can be run on variety of parallel computers. The experimental results on a cluster of Pentium II computers with PVM3 and ADAPTOR compilation system are presented. Efficiency of the parallel Reinsch algorithm is about eighty percent.
- Full text in SWF PDF format

Article 10EN: A uniform estimate for the modulus of continuity of starlike mappings
97-103

Nikos S. Stylianopoulos, Elias Wegert

Let f : D → Ω be a conformal mapping of the unit disk D onto a starlike domain G normalized by f(0) = 0. In this note we derive the uniform estimate

ωφ(δ) ≤ (π logR  + 6) / |logδ|

for the modulus of continuity ωφ(δ) of the boundary correspondence function φ := arg f |D for all starlike domains G with D   G   RD. An example shows that this estimate gives the correct order with respect to δ.

- Full text in SWF PDF format

Article 11EN: Errata to "Multivalent Harmonic Starlike Functions"
105-

Om P. Ahuja, Jay M. Jahangiri

(Errata to "Multivalent Harmonic Starlike Functions"; Ann. Univ. Mariae Curie-Skłodowska Sect. A, 55 (2001), 1­13)

In Section five of the above named paper "m(1 - α)" needs to replace "m - α" which appeared twice in the denominators of inequality (14) and two more times in the numerators of the equations after Theorem 8.

- Full text in SWF PDF format

Volume 55 - 2001

Article 01EN: Multivalent harmonic starlike functions
1-13

Om P. Ahuja, Jay M. Jahangiri

We give sufficient coefficient conditions for complex-valued harmonic functions that are multivalent, sense-preserving, and starlike in the unit disk. These coefficient conditions are also shown to be necessary if the coefficients of the analytic part of the harmonic functions are negative and the coefficients of the co-analytic part of the harmonic functions are positive. We also determine the extreme points, distortion and covering theorems, convolution and convex combination conditions for these functions.
- Full text in SWF PDF format

Article 02EN: Torsions of connections on higher order tangent bundles
15-22

Miroslav Doupovec, Jan Kurek

The torsion of a connection on a natural bundle is defined as the Frölicher-Nijenhuis bracket of some natural affinor and the connection itself. Using the complete description of all natural affinors on r-th order tangent bundles, we determine all torsions of connections on such bundles.
- Full text in SWF PDF format

Article 03EN: On the growth of the derivative of Qp functions
22-38

Cristóbal González, María A. Márquez

In this paper we investigate some properties of the derivative of functions in the Qp spaces. We first show that T(r,f'), the Nevanlinna characteristic of the derivative of a function f  Qp, 0 < p < 1, satisfies

01 (1-r) p exp(2T(r,f'))dr < ∞,

and that this estimate is sharp in a very strong sense, extending thus a similar result of Kennedy for functions in the Nevanlinna class.

We also obtain several results concerning the radial growth of the derivative of Qp functions.

- Full text in SWF PDF format

Article 04EN: n-dimensional Markov - like algorithms
39-52

Zdzisław Grodzki, Jerzy Mycka

New class MAnk1, ... , kn, n ≥ 1, of n-dimensional Markov-like algorithms is introduced. The equivalence of this class of algorithms and the class MNA of Markov normal algorithms is discussed.
- Full text in SWF PDF format

Article 05EN: An estimate of the growth of spirallike mappings relative to a diagonal matrix
53-59

Hidetaka Hamada, Gabriela Kohr

In this paper we give an upper estimate of the growth of a component of normalized spirallike mappings relative to a diagonal matrix on the Euclidean unit ball.
- Full text in SWF PDF format

Article 06EN: Subordination chains and univalence of holomorphic mappings on bounded balanced pseudoconvex domains
61-80

Hidetaka Hamada, Gabriela Kohr

Let Ω be a bounded balanced pseudoconvex domain with C1 plurisubharmonic defining functions in Cn. We introduce a subclass of univalent mappings on Ω, called the class of mappings which have the parametric representation and we study several properties of these mappings, concerning the growth, covering and distortion results. We give some consequences, examples and conjectures.
- Full text in SWF PDF format

Article 07EN: On maximum modulus of polynomials
81-84

V. K. Jain

For a polynomial p(z) of degree n, it is known that

|p(Re)| + |q(Re)|  ≤  (Rn + 1){max|z|=1|p(z)|},

R ≥ 1 and 0 ≤ θ ≤ 2π where

q(z) = znp(1/ z‾).

We obtain a refinement, as well as a generalization, of this inequality.

- Full text in SWF PDF format

Article 08DE: Zur möglichst konformen Spiegelung
85-94

Reiner Kühnau

We construct the extremal quasiconformal reflection in the set E consisting of a circular arc and an isolated point. We use the famous Teichmüller "Verschiebungssatz". The set of fixpoints is a quasicircle which therefore has the same "reflection coefficient" as E.
- Full text in SWF PDF format

Article 09EN: Connections and torsions on TT*M
95-107

Miroslav Kureš

The connections on the bundle TT*M → T*M are investigated and the results concerning liftings of connections are summarized. General torsions of a connection are defined as the Frölicher-Nijenhuis brackets of the associated horizontal projection and natural affinors on this bundle. All general torsions on TT*M are derived. Specially, the torsions of linear connections and lifted classical linear connections are described geometrically.
- Full text in SWF PDF format

Article 10EN: Liftings of 1-forms to the bundle of affinors
109-113

Włodzimierz M. Mikulski

All natural operators T*  T*(T T*) over n-manifolds are described. Non-existence of canonical volume forms on some natural bundles is deduced.
- Full text in SWF PDF format

Article 11EN: On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve
115-138

Dariusz Partyka, Ken-Ichi Sakan

We discuss conformally invariant pseudo-metrics on the class of all sense-preserving homeomorphisms of a given Jordan curve by means of the second module of a quadrilateral.
- Full text in SWF PDF format

Article 12EN: Discrete harmonic measure, Green's functions and symmetrization: a unified probabilistic approach
139-174

Alexander R. Pruss

We use probabilistic methods based on the work of Haliste (1965) to obtain various new versions of theorems of Baernstein (1974) on the effects of circular symmetrizations on harmonic measure and Green's functions. Our results are quite general and include a number of cases of symmetrization in discrete settings. For instance, in the setting of the discrete cylinder Z × Zm we obtain complete generalized analogues of Baernstein's results on harmonic measure and Green's functions, and even get a discrete version of Beurling's (1933) shove theorem.
- Full text in SWF PDF format

Article 13EN: On the size of the ideal boundary of a finite Riemann surface
175-180

Gerald Schmieder, Masakazu Shiba

The ideal boundary of a non-compact Riemann surface R0 becomes visible if R0 is embedded into some compact surface R which naturally should have the same genus g as R0. All these compactifications of R0 can be compared in a certain quotient space of Cg. With respect to the canonical metric in this space the diameters of all models of the ideal boundary of R0 are known to be bounded (cf. [4]) by a number depending only on R0.

In this paper we prove that the diameter of each component has either a positive lower bound, depending only of R0, or this component appears to be a single point in any compactification R.

- Full text in SWF PDF format

Article 14EN: A nonlinear Abelian ergodic theorem for asymptotically nonexpansive mappings in a Hilbert space
181-190

Takeshi Yoshimoto

Let C be a closed convex subset of a real Hilbert space and let T be an asymptotically nonexpansive nonlinear self-mapping of C. We prove a nonlinear Abelian ergodic theorem which deals with the weak convergence of the Abelian averages Ar[T]x, 0 < r < 1, of the iterates {T nx} for each x in C.
- Full text in SWF PDF format

Volume 54 - 2000

Article 01EN: A survey of applications of the Julia variation
1-20

Roger W. Barnard, Kent Pearce, Carolyn Campbell

This is an introductory survey on applications of the Julia variation to problems in geometric function theory. A short exposition is given which develops a method for treating extremal problems over classes F of analytic functions on the unit disk D for which appropriate subsets Fn can be constructed so that (i) and (ii) for each f  Fn a geometric constraint will hold that f(D) will have at most n "sides". Applications of this method which have been made to problems in the literature are reviewed, e.g., Netanyahu's problems about the distortion theorems for starlike and convex functions constrained to contain a fixed disk; Goodman's problems about omitted values for classes of univalent functions; integral means estimates for derivatives of convex functions; maximization problems for functionals on linear fractional transforms of convex and starlike functions.
- Full text in SWF PDF format

Article 02EN: On the valency of a polynomial in HH
21-25

Daoud Bshouty, Walter Hengartner

In this note we discuss the valency of a function f which is the product of an analytic polynomial and the conjugate of another analytic polynomial.
- Full text in SWF PDF format

Article 03EN: A coefficient product estimate for bounded univalent functions
27-44

Andrzej Ganczar, Dmitri V. Prokhorov, Jan Szynal

For given integers m and n, 2 < m < n, we consider the problem max |aman| in the class S(M) of holomorphic, univalent and bounded functions f(zz + a2 z2 + ... in the unit disk |z< 1. We prove that max |aman| is realized by the Pick function for M close to 1 iff (m - 1) and (n - 1) are relatively prime.
- Full text in SWF PDF format

Article 04EN: On some conjectures concerning bounded univalent
45-52

Zbigniew J. Jakubowski

Let S denote the class of all functions of the form F(z= z A2z2  + ... + Anzn + ... holomorphic and univalent in the unit disc Δ = {z   C: |z< 1}, SR - its subclass consisting of functions with real coefficients (An = An, n = 2, 3, ...). Let also S(M) and SR(M), M > 1, denote the corresponding subclasses of functions satisfying the condition |F(z)| M for  Δ. The main aim of the paper is to remind a few conjectures concerning some functionals defined in the classes S(M) or SR(M) and their solutions. We shall formulate certain new problems as well.
- Full text in SWF PDF format

Article 05DE: Über die Grunskyschen Koeffizientenbedingungen
53-60

Reiner Kühnau

We will derive a sharpened form of the Grunsky coefficient inequalities which guarantee for a given mapping  Σ the existence of a quasiconformal extension with an explicit dilatation bound.
- Full text in SWF PDF format

Article 06EN: Regularity theorems for linearly invariant families of holomorphic mappings in Cn
61-73

Piotr Liczberski, Victor V. Starkov

The authors give a theorem concerning results which state that the mapping having the highest rate of growth of the Jacobian, in a linearly invariant family of locally biholomorphic mappings, have this growth regular.
- Full text in SWF PDF format

Article 07EN: Another proof of boundedness of the Cesàro operator on H p
75-78

Maria Nowak

We give a new short proof of the boundedness of the Cesàro operator on H p, 0 < p < ∞.
- Full text in SWF PDF format

Article 08EN: On bounded univalent functions and the angular derivative
79-106

Christian Pommerenke, Alexander Vasil'ev

In this paper we study bounded univalent functions f(z) that map the unit disk into itself such that f(0) = 0. In particular we are concerned with the functions for which the angular limit and the angular derivative exist at certain points of the unit circle. For such functions we obtain several explicit estimates many of which are sharp. We apply two different methods to derive them. One is based on the the Schiffer-Tammi analogue of the Grunsky inequality, the other one uses the method of modules of curve families and the extremal partition of domains.
- Full text in SWF PDF format

Article 09EN: On the growth of polynomials not vanishing in the unit disc
107-115

Mohammed A. Qazi, Qazi I. Rahman

Let Pn* denote the class of all polynomials of degree at most n not vanishing in the open unit disc. Furthermore, let 0 ≤ r < R ≤ 1. We obtain some sharp lower and upper bounds for |f(r)|/{|f(R)|} when f belongs to Pn*. In our investigations we make essential use of certain properties of functions analytic and bounded in the unit disc.
- Full text in SWF PDF format

Article 10EN: On starlike functions of order λ   [1/2,1)
117-123

Stephan Ruscheweyh, Luis Salinas

Let zf be starlike of order λ   [½,1), and denote by sn(f,z) the n-th partial sum of the Taylor expansion of f about the origin. We then prove that

sn(f,z)/f(z)     (1 - z)2λ - 2,    n N.

Applications to Gegenbauer polynomial sums are mentioned, and a new concept of "stable" functions is briefly discussed.

- Full text in SWF PDF format

Article 11EN: On the Möbius distance
125-131

Gerald Schmieder

In this paper we try to initiate an analytic approach of an extension of Schwarz's Lemma to holomorphic functions defined on multiply connected domains as studied by Ahlfors and Grunsky.
- Full text in SWF PDF format

Article 12EN: Optimization problems for convex functions
133-148

Wojciech Szapiel

Assume that A, B are non-empty convex subsets of a real linear space and let f : A → R be a given convex function. When B is determined by a finite number of convex constraints, there are known necessary and sufficient conditions for p   AB to be a solution of the constrained problem f(pmin f(AB) considered as the unconstrained problem for a suitable Lagrange function over the set A. The purpose of this article, except a short presentation of the mentioned convex programming, is to discuss in detail a quite different problem of maximizing f over the set AB.
- Full text in SWF PDF format

Article 13EN: On zeros of Bloch functions and related spaces of analytic functions
149-158

Piotr Waniurski

In this paper we consider some problems for zero sets of Bloch functions and A p functions. We improve some necessary conditions for ordered zero sequences and show that they are best possible.
- Full text in SWF PDF format