单位球B^(n)上复数λ阶的g-星形映射  

g-Starlike Mappings of Complex Orderλon the Unit Ball Bn

作　　者：胡春英[1] 刘太顺[2] 王建飞 Chun Ying HU;Tai Shun LIU;Jian Fei WANG(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,P.R.China;Department of Mathematics,Huzhou Teachers College,Huzhou 313000,P.R.China)

机构地区：[1]华侨大学数学科学学院,泉州362021 [2]湖州师范学院理学院,湖州313000

出　　处：《数学学报（中文版）》2023年第1期149-160,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12071161,11971165,11971182);福建省自然科学基金资助项目(2020J01073,2019J01066)。

摘　　要：本文引入单位球B^(n)■C^(n)上复数λ阶的g-星形映射族,统一了复数λ阶的殆星映射和g-星形映射.应用Loewner链方法,建立了该映射族的增长定理,给出了k次齐次多项式P_(k)的数量特征,证明了B^(n)上扰动的Roper-Suffridge算子ΦP_(k)(f)(z)=(f(z_(1))+Pk(z_(0))f’(z_(1)),[f’(z_(1))]^(1/kz_(0))^(T)保持复数入阶的g-星形性.本文结果不仅推广了B^(n)上不同星形映射子族的增长定理,而且给出了扰动项P_(k)更为简洁的几何特征.In this paper,a subclass of g-starlike mappings of complex orderλon the unit ball B^(n)■C^(n)is introduced,which unifies almost starlike mappings of complex orderλand g-starlike mappings.The growth theorem for g-starlike mappings of complex orderλis established by using the parameter method of Loewner chains.By giving scalar conditions of homogenous polynormials of degree k,we prove that the modified Roper-Suffridge extension operator on the unit ball Bngiven byΦP_(k)(f)(z)=(f(z_(1))+Pk(z_(0))f’(z_(1)),[f’(z_(1))]^(1/kz_(0))^(T)preserves the property of g-starlike mappings of complex orderλ.Our results not only generalize some well-known growth theorems of different classes of star like mappings on Bn,but also give more concise geometric characteristics of polynomial Pk.

关 键 词：全纯映射 复数λ阶的g-星形映射 增长定理 ROPER-SUFFRIDGE算子 

分 类 号：O174.5[理学—数学]