On biholomorphic mappings in complex Banach spaces
type: Item
instance of: scholarly article
title: On biholomorphic mappings in complex Banach spaces
zbMATH Open document ID: 1238.46039
DOI: 10.1216/RMJ-2011-41-6-2069
author: Qing-Hua Xu
author: Taishun Liu
published in: Rocky Mountain Journal of Mathematics
publication date: 2012-01-12T00:00:00Z
review text: The authors generalize the concept of mappings with \(g\)-parametric representation introduced by \textit{G. Kohr} in [Rev. Roum. Math. Pures Appl. 46, No. 6, 743--760 (2001; Zbl 1036.32014)] in the case of \(\mathbf{C}^n\) to biholomorphic normalized maps of the unit ball of any complex Banach space, giving rise to the classes \(\mathcal{M}_g\). They also extend the concept of strong starlikeness of order \(\alpha > 0\) to the Banach space setting for holomorphic maps defined on the unit ball in a natural manner. The main results are sharp growth estimates, distortion and covering theorems implying and unifying several known results concerning the classes \(\mathcal{ M}_g\) in extended form in infinite dimensions.
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 32H99
Mathematics Subject Classification ID: 32A30
zbMATH DE Number: 5996742
zbMATH Keywords: coefficient estimation
zbMATH Keywords: starlike mapping
zbMATH Keywords: starlike mapping of order \(\alpha\)
zbMATH Keywords: almost starlike mapping of order \(\alpha\)
zbMATH Keywords: strongly starlike mapping of order \(\alpha\)
zbMATH Keywords: strongly starlike mapping
reviewed by: László Stachó
MaRDI profile type: Publication
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full work available at URL: rmj-2011-41-6-2069
OpenAlex ID: W1996175693
description: scientific article; zbMATH DE number 5996742