International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 8, Pages 1171-1187
doi:10.1155/IJMMS.2005.1171
On the generalized Roper-Suffridge extension operator in Banach spaces
Mingsheng Liu1
and Yucan Zhu2
1School of Mathematical Science, South China Normal University, Guangzhou, Guangzhou 510631, China
2Department of Mathematics, Fuzhou University, Fuzhou, Fujian 350002, China
Abstract
The generalized Roper-Suffridge extension operator in Banach spaces is introduced. We prove that this operator preserves the starlikeness on some domains in Banach spaces and does not preserve convexity in some cases. Furthermore, the growth theorem and covering theorem of the corresponding mappings are given. Some results of Roper and Suffridge and Graham et al. in ℂn are extended to Banach spaces.