一类解析函数的星像和单叶半径

The Radius of Starlikeness and Univalence of Certain Analytic Functions

设N_α表示在单位园内解析,形如p(z)=1+α_1z+…,且满足条件(0≤α≤2)的函数类。在本文,对于满足条件f(z)/g(z)∈N_α的解析函数f(z)=z+a_2z^2+…,我们决定了它的星像半径和单叶半径:其中g(z)=z+…分别是: (ⅰ) g(z)满足g(z)/z∈N_β(0≤β≤2); (ⅱ) g(z)满足Re{g(z)/z}>1/2; (ⅲ) g(z)是β阶星像函数。

Let N_α denote the class of functions of the form p (z)=1+α_1z+...,which are analytic in the unit disc and satisfy [arg p (z)]<πα/2 for some α (0≤α≤2). In this paper, we determine the radius of univalence (and starlikenes) of functions f(z) that satisfy f(z)/g(z)∈N_α for a function g(z) being(ⅰ) g (z) satisfies g(z)/z ∈N_β (0≤β≤2);(ⅱ) g (z) satisfies Re {g(z)/z }>1/2;(ⅲ g (z) is starlike of order β.