NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

doi:10.1007/s10473-019-0609-4

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1579-1588.doi: 10.1007/s10473-019-0609-4

NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

彭志刚¹, Milutin OBRADOVI?²

1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2. Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Serbia

收稿日期:2018-07-27 修回日期:2019-05-16 出版日期:2019-12-25 发布日期:2019-12-30
通讯作者: Zhigang PENG,E-mail:obrad@grf.bg.ac.rs E-mail:obrad@grf.bg.ac.rs
作者简介:Milutin OBRADOVIĆ,E-mail:obrad@grf.bg.ac.rs
基金资助:
The first author was supported by the Key Laboratory of Applied Mathematics in Hubei Province, China. The second author was supported by MNZZS (ON174017, Serbia).

NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

Zhigang PENG¹, Milutin OBRADOVI?²

1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2. Department of Mathematics, Faculty of Civil Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000, Serbia

Received:2018-07-27 Revised:2019-05-16 Online:2019-12-25 Published:2019-12-30
Contact: Zhigang PENG,E-mail:obrad@grf.bg.ac.rs E-mail:obrad@grf.bg.ac.rs
Supported by:
The first author was supported by the Key Laboratory of Applied Mathematics in Hubei Province, China. The second author was supported by MNZZS (ON174017, Serbia).

摘要/Abstract

摘要： Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈ C:|z|<1}, normalized by the conditions f(0)=0 and f'(0)=1. Let U denote the set of all functions f ∈ A satisfying the condition
|(z/f(z))² f'(z) -1|<1 for z ∈ D.
Let Ω be the class of all f ∈ A for which
|zf'(z) -f(z)|<1/2, z ∈ D.
In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.

关键词: analytic, univalent, coefficient, Hadamard product

Abstract: Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈ C:|z|<1}, normalized by the conditions f(0)=0 and f'(0)=1. Let U denote the set of all functions f ∈ A satisfying the condition
|(z/f(z))² f'(z) -1|<1 for z ∈ D.
Let Ω be the class of all f ∈ A for which
|zf'(z) -f(z)|<1/2, z ∈ D.
In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.

Key words: analytic, univalent, coefficient, Hadamard product

中图分类号:

30C45

彭志刚, Milutin OBRADOVI?. NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS[J]. 数学物理学报(英文版), 2019, 39(6): 1579-1588.

Zhigang PENG, Milutin OBRADOVI?. NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS[J]. Acta mathematica scientia,Series B, 2019, 39(6): 1579-1588.

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NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS

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