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

doi:10.1016/S0252-9602(16)30116-3

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 69-78.doi: 10.1016/S0252-9602(16)30116-3

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

彭志刚, 钟广祯

Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China

收稿日期:2015-11-06 修回日期:2016-03-18 出版日期:2017-02-25 发布日期:2017-02-25
作者简介:Zhigang PENG,Gangzhen ZHONG,E-mail:pengzhigang@hubu.edu.cn;E-mail:Zachery626@163.com
基金资助:
Supported by the Key Laboratory of Applied Mathematics in Hubei Province, China.

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

Zhigang PENG, Gangzhen ZHONG

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.

摘要/Abstract

摘要：

Let A be the space of functions analytic in the unit disk D={z:|z|<1}. Let U denote the set of all functions f∈A 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 f∈A 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.

关键词: univalent function, Starlike function, Hadamard product, extreme point, support point

Abstract:

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

彭志刚, 钟广祯. SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES[J]. 数学物理学报(英文版), 2017, 37(1): 69-78.

Zhigang PENG, Gangzhen ZHONG. SOME PROPERTIES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS DEFINED BY DIFFERENTIAL INEQUALITIES[J]. Acta mathematica scientia,Series B, 2017, 37(1): 69-78.

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

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

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