关于解析函数的某类子族的若干性质

Some properties of a subclass of analatic functions

设R(α,β,γ)表示在单位圆U={z∈C:|z|<1}内形为f(z)=z+a_2z^2+…且满足条件R{αf′(z)+βzf′(z)}>γ(β>0;0≤γ<α≤1;z∈U)的解析函数族;本文我们给出了函数族R(α,β,γ)的系数充要条件,星象和凸象半径,极值点以及偏差估计.所得到的结果推广了一些相关文献的结果.

Let R （α,β,γ） denote the class of funtions of the formf（z） = z ＋ a2z^2 ＋…, Which are analytic in the unit disk U={z∈C;｜z｜〈1} and satisfying the condition R｜αf（z）＋βzf＂（z）}〉γ （β〉0;0≤γ〈α≤1;z∈U）. In the present paper, we provide necessary and sufficient coefficient conditions, radius of starlikeness and convexity, extreme points, and distortion bounds for funtions belonging to the class. The results presented here would provide extensions of those given in earlier works.