首页 | 本学科首页   官方微博 | 高级检索  
     检索      


The generalized Roper-Suffridge extension operator in Banach spaces (II)
Authors:Yucan Zhu  Mingsheng Liu
Institution:a Department of Mathematics, Fuzhou University, Fuzhou, 350002 Fujian, PR China
b Department of Mathematics, South China Normal University, Guongzhou, 510631 Guangdong, PR China
Abstract:In this paper, we generalize the Roper-Suffridge extension operator from Cn to Banach spaces. It is proved that this operator preserves the biholomorphic ? starlikeness on some domains in Banach spaces. From these, we may construct a lots of concrete examples about biholomorphic ? starlike mappings on some domains Ω in Cn, or Hilbert spaces, or Banach spaces from univalent ? starlike functions on the unit disc U in C. Meanwhile, the growth theorems of the corresponding mappings are given. Some results of Gong and Liu, Roper and Suffridge, Graham et al. in Cn are extended to Hilbert spaces or Banach spaces.
Keywords:Biholomorphic ? starlike mapping  Biholomorphic convex mapping  Biholomorphic starlike mapping  Roper-Suffridge extension operator
本文献已被 ScienceDirect 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号