Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (1): 69-78.doi: 10.1016/S0252-9602(16)30116-3

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SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES

Zhigang PENG, Gangzhen ZHONG   

  1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China
  • Received:2015-11-06 Revised:2016-03-18 Online:2017-02-25 Published:2017-02-25
  • About author:Zhigang PENG,Gangzhen ZHONG,E-mail:pengzhigang@hubu.edu.cn;E-mail:Zachery626@163.com
  • Supported by:

    Supported by the Key Laboratory of Applied Mathematics in Hubei Province, China.

Abstract:

Let A be the space of functions analytic in the unit disk D={z:|z|<1}. Let U denote the set of all functions fA satisfying the conditions f(0)=f'(0) 1=0 and
|f'(z)((z)/(f(z)))2-1|<1 (|z|< 1).
Also, let denote the set of all functions fA satisfying the conditions f(0)=f'(0)-1=0 and
|zf'(z)-f(z)|<(1)/(2) (|z|<1).
In this article, we discuss the properties of U and Ω.

Key words: univalent function, Starlike function, Hadamard product, extreme point, support point

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