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Acta Mathematica Sinica, English Series

, Volume 30, Issue 7, pp 1133–1144 | Cite as

Some radius problems related to a certain subclass of analytic functions

  • Oh Sang Kwon
  • Young Jae Sim
  • Nak Eun Cho
  • H. M. SrivastavaEmail author
Article

Abstract

For real parameters α and β such that 0 ≤ α < 1 < β, we denote by S(α, β) the class of normalized analytic functions which satisfy the following two-sided inequality:
$$\alpha < \Re \left( {\frac{{zf'(z)}} {{f(z)}}} \right) < \beta ,z \in \mathbb{U} $$
where \(\mathbb{U}\) denotes the open unit disk. We find a sufficient condition for functions to be in the class S(α, β) and solve several radius problems related to other well-known function classes.

Keywords

Analytic functions univalent functions starlike functions functions of bounded real positive real part radius problems 

MR(2010) Subject Classification

30C45 30C55 

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References

  1. [1]
    Amer, A., Darus, M.: On radius problems in the class of univalent functions. Internat. J. Pure Appl. Math., 73, 471–476 (2011)zbMATHMathSciNetGoogle Scholar
  2. [2]
    Aouf, M. K., Dziok, J., Sokół, J.: On a subclass of strongly starlike functions. Appl. Math. Lett., 24, 27–32 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Duren, P. L.: Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983Google Scholar
  4. [4]
    Kobashi, H., Kuroki, K., Owa, S.: Notes on radius problems of certain univalent functions. Gen. Math., 17(4), 5–12 (2009)zbMATHMathSciNetGoogle Scholar
  5. [5]
    Kuroki, K., Owa, S.: Notes on new class for certain analytic functions. RIMS Kôkyûroku, 1772, 21–25 (2011)Google Scholar
  6. [6]
    MacGregor, T. H.: A subordination for convex functions of order α. J. London Math. Soc. (Se. 2), 9, 530–536 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    Miller, S. S., Mocanu, P. T.: Differential Subordination: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, No. 225, Marcel Dekker Incorporated, New York and Basel, 2000Google Scholar
  8. [8]
    Noor, K. I., Arif, M.: Some radius problems for certain classes of analytic functions with fixed second coefficients. Nonl. Funct. Anal. Appl., 15, 79–85 (2010)zbMATHMathSciNetGoogle Scholar
  9. [9]
    Rønning, F.: Uniformly convex functions and a corresponding class of starlike functions. Proc. Amer. Math. Soc., 118, 189–196(1993)CrossRefMathSciNetGoogle Scholar
  10. [10]
    Sokół, J.: Coefficient estimates in a class of strongly starlike functions. Kyungpook Math. J., 49, 349–353 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  11. [11]
    Sokół, J.: Radius problems in the class SL*. Appl. Math. Comput., 214, 569–573 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  12. [12]
    Uyanik, N., Owa, S.: Note on radius problems for certain class of analytic functions. Fract. Calc. Appl. Anal., 13, 553–560 (2010)zbMATHMathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Oh Sang Kwon
    • 1
  • Young Jae Sim
    • 1
  • Nak Eun Cho
    • 2
  • H. M. Srivastava
    • 3
    Email author
  1. 1.Department of MathematicsKyungsung UniversityBusanRepublic of Korea
  2. 2.Department of Applied MathematicsPukyung National UniversityBusanRepublic of Korea
  3. 3.Department of Mathematics and StatisticsUniversity of VictoriaVictoriaCanada

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