复Banach空间上推广的Roper-Suffridge延拓算子  

THE GENERALIZED ROPER-SUFFRIDGE EXTENSION OPERATORS IN COMPLEX BANACH SPACE

作　　者：崔艳艳[1] 王朝君[1] 

机构地区：[1]周口师范学院数学与信息科学系,河南周口466001

出　　处：《数学杂志》2014年第3期515-520,共6页Journal of Mathematics

基　　金：国家自然科学基金资助(11271359;U1204618);河南省教育厅自然科学基金资助(2011B110034);河南省科技厅软科学项目(102400450003)

摘　　要：本文研究了推广的Roper-Suffridge算子保持一些双全纯映照子族的性质.利用一些双全纯映照子族的定义,得到了推广后的Roper-Suffridge算子在复Banach空间单位球上保持ρ次抛物形β型螺形映照及强α次殆星形映照的性质,由此得到复Hilbert空间上推广的Roper-Suffridge算子的相应性质,推广了已有的结论.In this paper, the authors prove that the extended Roper-Suffridge operators preserve the properties of some subclasses of biholomorphic mappings. By the definitions of some subclasses of biholomorphic mappings, we prove that the extended Roper-Suffridge operators preserve the properties of parabolic and spiralike mappings of type β and order ρ, strongly and almost starlike mappings of order α on the unit ball in complex Banach spaces, and thus we obtain the corresponding properties of the extended Roper-Suffridge operators in complex Hilbert spaces,which extend the known results.

关 键 词：ROPER-SUFFRIDGE算子 ρ次抛物形β型螺形映照 强α次殆星形映照 

分 类 号：O174.56[理学—数学]