关于一类具有负系数的广义单叶函数性质  

Properties of a class of generalized univalent functions with negative coefficients

作　　者：何涛[1] 周海燕[1] 李书海[1] HE Tao;ZHOU Hai-yan;LI Shu-hai(School of Mathematics and Statistics,Chifeng University,Chifeng 024000,P.R.C)

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024000

出　　处：《西南民族大学学报（自然科学版）》2018年第5期530-537,共8页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11561001);内蒙古自然科学基金资助项目(2014MS0101)

摘　　要：引进并研究了一类具有负系数的广义单叶函数.首先利用从属关系和微分方程方法讨论了该类中函数的积分表达式和系数不等式,由此推出偏差、覆盖、闭包定理和极值点.最后,讨论该类中函数的Hadamard卷积的封闭性质和包含关系.所得结果推广了负系数单叶函数性质,并得到一些新结果.A class of generalized univalent functions with negative coefficients are introduced and investigated. Firstly,the methods of subordination relationship and differential equation are used to discuss the integral expression and coefficient inequalities of functions belonging to the above class,and then the distortion theorem,covering theorem,closure theorem and extreme point are obtained. Finally,the closure properties and inclusion relations of Hadamard product of functions belonging to the above class are studied. The results obtained extend the properties of univalent functions with negative coefficients and also get some new results.

关 键 词：单叶函数 系数不等式 积分表达式 HADAMARD卷积 

分 类 号：O174.51[理学—数学]