On the generalized Roper-Suffridge extension operator in Banach spaces

Ming-Sheng Liu and Yu-Can Zhu

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-17

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 â„‚ n are extended to Banach spaces.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:706318

DOI: 10.1155/IJMMS.2005.1171

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