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


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.


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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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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