一族单叶函数的凸形半径

The Radius of Convexity of a Class of Univalent Functions

本文讨论了函数族:R(α,β)={f′(z)=1+sum from n=1 to ∞ b_az^n,|f′(z)-1|/|2β(f′(z)-α)-(f′(z)-1)|<1}当(α,β)=((1+AB)(1-A)^(-1),(1-A)/2)(0<A≤1,-1<B≤1)时,f(z)的系数估计和凸形半径,结果是准确的。

In this paper,the author discuss the class of functions:R(α,β)={f′(z) =1+som from ∞ to n=1 b_nz^n,丨f′(z)-1丨/丨2β(f′(z)-a)-(f′(z)-1)丨<1},if((α,β) =((1+AB)(1-A)^(-1),(1-A)/2)(0<A≤1,-1<B≤1),and obtain the sharp boundary of coefficients of f(z)and radius of convexity of f(z).