一个解析函数族的星形半径  

The Radius of Starlikeness of A Class of Analytic Functions

作　　者：蒋润荣[1] 

机构地区：[1]广西民族学院

出　　处：《纯粹数学与应用数学》1989年第5期91-93,共3页Pure and Applied Mathematics

摘　　要：设E(r)={Z:|Z|>r},E(1)简记作E。设函数F(Z)在E上具有展开式 F(Z)=Z+sum from n=1 to ∞ b_nZ^(-n) (1)由[1;P.19]知,We introduce notations E(γ)={Z:|Z|>γ}, E=E(1), and Suppose F(Z)=Z+(sum from =1 to ∞(bnZ^() (Z∈E)). It is considered in [2] that F(Z) is a starlike function in E(√ 2 ). The purpose of this paper is to extend this resut as follows: Let ∑(λ) denote the class of all functions F(Z)=Z+(sum from n=k to ∞(b_(?)Z^(?)(Z∈E), K≥0)) satistying condition (sum from (?)=k+1 to ∞(n-λ)|d_n(λ)|~2≤λ), where d_n(λ) is the coefficients of the series (F(Z)/Z)~λ=1+(sum from n=k+1 to ∞(d_n(λ)Z^(-n)). Then the radius of starlikeness of class ∑(λ) is the unique solution of equation λr^2(k+2)-2λr^2(k+1)+λr^2k-(k+1-λ)r^2+k-λ=0 in (1,∞).

关 键 词：解析函数 星形半径 单叶半径 

分 类 号：O174.55[理学—数学]