单叶解析函数的一类子族的增长、掩盖定理

Growth and covering theorems of one subclass of univalent analysis functions

在复平面单位圆盘内引入单叶解析函数的一类子族Dβα函数族,利用从属关系研究了当f(z)-z具有k+1阶零点时f(z)的增长、掩盖定理,并对f(z)的系数an(n=k+1,…,2k)进行了估计,其中当n=k+1时估计是精确的.

In this paper,a subclass of univalent analysis functions denoted by Dβα is introduced in the unit disc of the complex plane.We studied the growth and covering theorems of f（z）when f（z）-z has zero of k＋1 order.We also estimated the coefficient an（n=k＋1,…,2k） of f（z）,and proved that the bound is sharp when n equals to k＋1.