某些近于凸调和函数的解析性质和系数估计  

On the Analytic Properties and Coefficient Estimate for Close-to-Convex Harmonic Mappings

作　　者：黄赟[1] 黄心中[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2015年第4期478-483,共6页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11471128);福建省自然科学基金资助项目(2014J01013)

摘　　要：研究单位圆盘D上某些具有稳定近于凸的调和函数f(z)=h(z)+g(z)解析部分h(z)满足Re{1+zh″(z)/h′(z)}>c,-12<c≤0时的解析表示和系数估计表达式.对其复伸张w(z)为一次多项式时,给出了f(z)的稳定近于凸的判别条件,并且推广了Bshouty和Nagpal等的结果.特别地,当Re{1+zh″/h′}>c,-12<c≤0,w(z)=z2时,估计了f=h+g在单位圆盘上的稳定近于凸半径.Research analytic representing formula and coefficient estimates for h（z）with Re{1＋zh″（z）/h′（z）}c,-12c≤0,where his the analytic part of harmonic mappings f（z）=h（z）＋g（z）that are stable close-to-convex property on unit disk D.If the dilatation function w（z）is a linear function,the stable close-to-convex criterion is proved.The results improve the one made by Shouty and Nagpal.Moreover,we also obtain the stable close-to-convex radius estimate for f= h＋g with Re{1＋zh″（z）/h′（z）}c,-12c≤0and w（z）=z2 on the unit disk D.

关 键 词：调和函数 稳定近于凸 系数估计 单叶半径 

分 类 号：O174.51[理学—数学]