一类近于凸函数子族的研究

函数g（z）〈G（z），当且仅当存在单位开圆盘E内的解析函数w（z）∈B0，即满足：w（0）=0，｜w（z）｜〈1，使得g（z）=G（w（z））（z∈E），设PA，B]={p（z）：p（0）=1，p（z）在E内解析且满足p（z）〈1＋Az/1＋Bz,-1≤B〈A≤1，一个函数g（z）∈CA，B]当且仅当（zg＇（z））＇/g＇（z）〈1＋Az/1＋Az.函数族KB＇A，B]={f（z）：f（0）=f＇（0）-1=0，f（z）在E内解析g（z）∈CA，B]，且Re{zf＇（z）/g（z）}〉B,-1≤B〈A≤1}，这是近于凸函数的一个子集，从而这些函数是单叶的．利用Janowski介绍的函数类PA，B]的性质，参考Khalida Inayat Noor研究CB＋A，B]的方法，研究这个函数族系数估计和半径问题，同时讨论KB’A，B]与其他单叶函数子族的关系．

A subclass of close-to-convex functions

A function g（z）〈G（z） if and only if it exited is a w（z）∈B0, where w（0）=0,｜w（z）｜〈1 , so that g（z）=G（w（z））（z∈E）.Let PA,B], -1≤B〈A≤1, denoted the class of functions p（z） ： p（0）=1, analytic in the unit open disk E, such that p（z） was subordinate to 1＋Az/1＋Bz.A function g（z）was said to belong to the class CA,B]if and only if （zg＇（z））＇/g＇（z） was in PA, B], KBA, B]-the class of analytic functions f（z）,where f（0）=f＇（0）-1=0, regular in E satisfying the condition. Re {zf＇（z）/g（z）}〉B, g∈CA,B], -1≤B〈A≤1.These functions in this class were close-to-convex and hence univalent. With the help of the new Class P-A,B]which introduced by Janowski, we studied its relationship with other functions. Co-efficient problem, distortion theorems, radius of convexity and other properties were solved.