某类解析函数的单叶性半径

On the Univalent Radius of Certain Analytic Functions

设F(z)是一单位圆盘D内的正规化的单叶函数.f(z)=11+cz1-c[zcF(z)]′,c=1,2,3,…,该文讨论F(z)分别为α级星形函数,α级凸函数时f(z)的单叶性半径,其中0≤α<1,并进一步得到了当Re{F′(z)}>α,z∈D时,使得Re{f′(z)}>β,0≤β<1成立的最大半径.这些结果都是最佳的.

Let F（z） be a regular and univalent function in the unit disk D = {z： ｜ z ｜〈 1} and let f（z） =1＋c/1z^1-c[z^cF（z）]＇. The paper deals with the mapping properties off（z） when F（z） is starlike of order convex of α andF（z）fitsRe{F＇（z）} 〉 α,0≤α 〈1. For example, if F（z） is starlike of order a , then the disk in which β, α≤β〈 l 〈 a 〈 1 is determined. All the results are sharp.