关于具有对称共轭点的双曲余弦单叶调和函数类的研究  

On the Classes of Univalent Harmonic Functions with the Symmetric Conjugate Point and Hyperbolic Cosine Function

作　　者：马丽娜 李书海 汤获 张海燕 MA Li-na;LI Shu-hai;TANG Huo;ZHANG Hai-yan(Institute of Basic Mathematics,School of Mathematics and Computer Science,Chifeng University,Chifeng 024000,China)

机构地区：[1]赤峰学院数学与计算机科学学院基础数学研究所,内蒙古赤峰024000

出　　处：《数学的实践与认识》2021年第18期246-260,共15页Mathematics in Practice and Theory

基　　金：内蒙古高等学校科学研究项目(NJZY20198,NJZZ19209,NJZY20200);内蒙古自然科学基金(2020MS01011,2019MS01023);赤峰市自然科学科研课题(SZR21002);赤峰学院科研创新团队-“复分析与非线性动力系统科研创新团队”(cfxykycxtd202005);赤峰学院青年科研基金项目(cfxyqn202133);赤峰学院重点实验室建设项目(CFXYZD202004)。

摘　　要：引入了解析部分具有对称共轭点的双曲余弦函数的单叶调和函数类.首先,得到了该函数类解析部分的偏差定理及系数估计.根据解析部分与共轭解析部分间的关系,由此得到了函数类的几何性质,如系数估计,偏差定理,积分表达式,Jacobian估计,增长条件及覆盖定理.特别地,画出了极值函数的图像,更好的反映了函数的性质.In this paper,some classes of univalent harmonic functions are introduced,the analytic parts of which are hyperbolic cosine starlike(or convex) functions with respect to the symmetric conjugate points.First of all,we get the distortion theorems and the coefficients estimates of analytic parts.According to the relationships of the analytic part and the coanalytic part,the geometric properties,such as coefficient estimates,distortion theorems,integral expressions,Jacobian estimates,growth conditions and covering theorem of the classes are obtained.In particular,we draw the figure of extremum functions to better reflect the geometric properties of the classes.

关 键 词：调和函数 双曲余弦 从属 对称共轭点 系数估计 偏差定理 

分 类 号：O174.51[理学—数学]