View More View Less
  • 1 University of Rzeszow, 35-310 Rzeszow, Poland
  • 2 Menoufia University, Shebin Elkom 32511, Egypt
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

Abstract

By making use of the pre-Schwarzian norm given by

f=supzU(1|z|2)|f(z)f(z)|,
we obtain such norm estimates for Hohlov operator of functions belonging to the class of uniformly convex functions of order α and type β. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in . Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

  • [1]

    Becker, J., Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen, Journal für die reine und angewandte Mathematik, 255 (1972), 2343 (in German).

    • Search Google Scholar
    • Export Citation
  • [2]

    Becker, J., Pommerenke, Ch., Schlichtheitskriterien und Jordangebiete, Journal für die reine und angewandte Mathematik, 354 (1984), 7494.

    • Search Google Scholar
    • Export Citation
  • [3]

    Bernardi, S. D., Convex and starlike univalent functions, Transactions of the American Mathematical Society, 135 (1969), 429446.

  • [4]

    Bharati, R., Parvatham, R., Swaminathan, A., On subclasses of unifomly convex functions and a corresponding class of starlike functions, Tamkang Journal of Mathematics, 28 (1997), 1732.

    • Search Google Scholar
    • Export Citation
  • [5]

    Bulboacă, T., Differential Subordinations and Superordinations. New Results, House of Scientific Book Publ., Cluj-Napoca, 2005.

  • [6]

    Duren, P. L., Univalent Functions, Springer-Verlag, New York, 1983.

  • [7]

    Dziok, J., Srivastava, H. M., Classes of analytic functions associated with the generalized hypergeometric function, Applied Mathematics and Computation, 103 (1999), 113.

    • Search Google Scholar
    • Export Citation
  • [8]

    Goodman, A. W., On uniformly convex functions, Annales Polonici Mathematici, 56 (1991), 8792.

  • [9]

    Goodman, A. W., On uniformly starlike functions, Journal of Mathematical Analysis and Applications, 155 (1991), 364370.

  • [10]

    Hohlov, Yu. E., Operators and operations in the class of univalent functions, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 10 (1978), 8389 (in Russian).

    • Search Google Scholar
    • Export Citation
  • [11]

    Hornich, H., Ein Banachraum analytischer Funktionen in Zusammenhang mit den schlichten Funktionen, Monatshefte für Mathematik, 73 (1969), 3645.

    • Search Google Scholar
    • Export Citation
  • [12]

    Kanas, S., Wisniowska, A., Conic regions and k-uniform convexity, Journal of Computational and Applied Mathematics, 105 (1999), 327336.

    • Search Google Scholar
    • Export Citation
  • [13]

    Kanas, S., Wisniowska, A., Conic regions and k-starlike functions, Revue Roumaine de Mathématique Pures et Appliquées, 45 (2000), 647657.

    • Search Google Scholar
    • Export Citation
  • [14]

    Kim, Y. C., Sugawa, T., Growth and coefficient estimates for uniformly locally univalent functions on the unit disk, Rocky Mountain Journal of Mathematics, 32 (2002), 179200.

    • Search Google Scholar
    • Export Citation
  • [15]

    Kim, Y. C., Ponnusamy, S., Sugawa, T., Mapping properties of nonlinear integral operators and pre-Schwarzian derivatives, Journal of Mathematical Analysis and Applications, 299 (2004), 433447.

    • Search Google Scholar
    • Export Citation
  • [16]

    Ma, W., Minda, D., Uniformly convex functions, Annales Polonici Mathematici, 57 (1992), 166175.

  • [17]

    Ma, W., Minda, D., A unified treatment of some special classes of univalent functions. in Proceedings of the conference on complex analysis, Z. Li, F. Ren, L. Lang and S. Zhang (Eds.), Int. Press, (1994), 157169.

    • Search Google Scholar
    • Export Citation
  • [18]

    Miller, S. S., Mocanu, P. T., Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Appl. Math., vol. 255, Marcel Dekker, Inc., New York, 2000.

    • Search Google Scholar
    • Export Citation
  • [19]

    Rønning, F., On starlike functions associated with parabolic regions, Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, 45 (1991), 117122.

    • Search Google Scholar
    • Export Citation
  • [20]

    Rønning, F., Unifomly convex functions and a corresponding class of starlike functions, Proceedings of the American Mathematical Society, 118 (1993), 190196.

    • Search Google Scholar
    • Export Citation
  • [21]

    Ruscheweyh, St., Convolutions in Geometric Function Theory, Les Presses de l'Université de Montréal, Montréal, 1982.

  • [22]

    Ruscheweyh, St., Sheil-Small, T., Hadamard products of schlicht functions and the Polya-Schoenberg conjecture, Commentarii Mathematici Helvetici, 48 (1973), 119135.

    • Search Google Scholar
    • Export Citation
  • [23]

    Ruscheweyh, St., Singh, V., On the order of starlikeness of hypergeometric functions, Journal of Mathematical Analysis and Applications, 113 (1986), 111.

    • Search Google Scholar
    • Export Citation
  • [24]

    Silverman, H., Univalent functions with negative coefficients, Proceedings of the American Mathematical Society, 51 (1975), 109116.

  • [25]

    Silverman, H., Starlike and convexity properties for hypergeometric functions, Journal of Mathematical Analysis and Applications, 172 (1993), 574581.

    • Search Google Scholar
    • Export Citation
  • [26]

    Srivastava, H. M., Owa, S. (Editors), Current Topics in Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, 1992.

    • Search Google Scholar
    • Export Citation

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE

 

  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • SCOPUS
  • The ISI Alerting Services

 

Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu