NEW RESULTS FOR A CLASS OF UNIVALENT FUNCTIONS  

作　　者：Zhigang PENG Milutin OBRADOVIC 彭志刚;Milutin OBRADOVIC(Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China;Department of Mathematics,Faculty of Civil Engineering,University of Belgrade,Bulevar Kralja Aleksandra 73,11000,Serbia)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2019年第6期1579-1588,共10页数学物理学报（B辑英文版）

基　　金：supported by the Key Laboratory of Applied Mathematics in Hubei Province,China;supported by MNZZS(ON174017,Serbia)

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))^2f'(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.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))~2f’(z)-1|<1 for z∈D.Let ? 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 ? are obtained.

关 键 词：ANALYTIC UNIVALENT COEFFICIENT HADAMARD PRODUCT 

分 类 号：O17[理学—数学]