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Ukrainian Mathematical Journal

, Volume 70, Issue 8, pp 1288–1299 | Cite as

Sufficient Conditions for Bounded Turning of Analytic Functions

  • N. Tuneski
  • T. Bulboacă
Article
  • 8 Downloads

Consider a function f analytic in the open unit disk and normalized so that f(0) = f′(0) 1 = 0. The methods of the theory of first-order differential subordinations are used to obtain sufficient conditions for the function f to have bounded turning, i.e., for the real part of its first derivative to map the unit disk onto the right half plane. In addition, several open problems are posed.

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References

  1. 1.
    T. Bulboacă, Differential Subordinations and Superordinations. New Results, House Sci. Book Publ., Cluj-Napoca (2005).Google Scholar
  2. 2.
    P. L. Duren, Univalent Functions, Springer-Verlag (1983).Google Scholar
  3. 3.
    S. S. Miller and P. T. Mocanu, Differential Subordinations. Theory and Applications, Marcel Dekker, New York; Basel (2000).Google Scholar
  4. 4.
    S. S. Miller and P. T. Mocanu, “Differential subordinations and univalent functions,” Michigan Math. J., 28, 157–171 (1981).MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. S. Miller and P. T. Mocanu, “On some classes of first-order differential subordinations,” Michigan Math. J., 32, 185–195 (1985).MathSciNetCrossRefGoogle Scholar
  6. 6.
    R. W. Ibrahim and M. Darus, “Extremal bounds for functions of bounded turning,” Int. Math. Forum, 6, No. 33, 1623–1630 (2011).MathSciNetzbMATHGoogle Scholar
  7. 7.
    J. Krzyz, “A counterexample concerning univalent functions,” Folia Soc. Sci. Lublinensis, 2, 57–58 (1962).Google Scholar
  8. 8.
    N. Tuneski and M. Obradović, “Some properties of certain expression of analytic functions,” Comput. Math. Appl., 62, 3438–3445 (2011).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • N. Tuneski
    • 1
  • T. Bulboacă
    • 2
  1. 1.Skopje Saints Cyril and Methodius UniversitySkopjeMacedonia
  2. 2.Babe¸s-Bolyai UniversityCluj-NapocaRomania

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