某些调和函数类的单叶保向条件  

Conditions of Univalent and Sense Preserving for Some Classes of Harmonic Functions

作　　者：马丽娜 李书海 汤获 MA Li-na;LI Shu-hai;TANG Huo(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》2022年第2期197-205,共9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);赤峰学院重点实验室建设项目(cFxYzD202004);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)

摘　　要：在单复变函数的研究中,解析函数及调和函数的单叶性与保向性一直都是一个研究的主要问题.众所周知,调和函数f=h+g在单位圆盘U内局部单叶及保向当且仅当|h'(z)|>|g'(z)|.那么能否找到调和函数单叶保向的其它条件呢?引入了解析部分在不同区域上星象的调和函数的子类,并首次给出了相应函.数类上的调和函数单叶及保向的条件.所得结果进一步丰富几何函数论.In the study of functions for a complex variable,properties for univalent and sense preserving of analytic and harmonic functions have always been a major problem.It is well-known that harmonic function f=h+g is univalent and sense preserving in the unit disc U if and only if |h'(z)|>|g'(z)|.So,can we find other conditions of univalent and sense preserving for harmonic functions?In this paper,we introduce the subclasses of harmonic functions,the analytic parts of which are st ar like in different regions,and obtain the conditions of univalent and sense preserving for the first time.The results further enrich the theory of geometric functions.

关 键 词：调和函数 星象函数 单叶 保向 

分 类 号：O174.5[理学—数学]