两类推广的Roper-Suffridge算子的性质  

Property of Two Kinds of Generalized Roper-Suffridge Extension Operators

作　　者：王朝君[1] 崔艳艳[1] 朱思峰[1] 

机构地区：[1]周口师范学院数学与统计学院,河南周口466001

出　　处：《西南大学学报（自然科学版）》2014年第4期55-58,共4页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271359;U1204618);河南省教育厅科学技术研究重点项目(14B110015;14B110016);河南省科技厅科技发展计划项目(102400450003)

摘　　要：讨论两类推广的Roper-Suffridge算子保持双全纯映照子族的性质.从定义出发证明推广的Roper-Suffridge算子在Cn中单位球上和复Banach空间单位球上保持强α次殆星映照及α次准凸映照的性质,进而得到推广的Roper-Suffridge算子在Cn中单位球上和复Hilbert空间单位球上分别保持强星形性和α次准凸性.In this paper,the authors discuss that two kinds of generalized Roper-Suffridge extension operators preserve the property of the subclasses of biholomorphic mappings and,from the definition,prove the fact that the extended operators preserve the properties of strong and almost starlike mappings of orderα and quasi-convex mappings of orderαon the unit ball in Cn and in the complex Banach space.Then it is shown that the generalized operator keeps strongly starlikeness and quasi-convexity of orderαon the unit ball in Cn and in complex Hilbert space,respectively.

关 键 词：强α次殆星映照 α次准凸映照 ROPER-SUFFRIDGE算子 

分 类 号：O174.51[理学—数学]