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AMENABLE SEMIGROUPS OF NONLINEAR OPERATORS IN UNIFORMLY CONVEX BANACH SPACES

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  28 November 2018

KHADIME SALAME Open the ORCID record for KHADIME SALAME [Opens in a new window]
KHADIME SALAME*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada email [email protected], [email protected]
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Abstract

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In 1965, Browder proved the existence of a common fixed point for commuting families of nonexpansive mappings acting on nonempty bounded closed convex subsets of uniformly convex Banach spaces. The purpose of this paper is to extend this result to left amenable semigroups of nonexpansive mappings.

Keywords

amenabilityasymptotic centrecommon fixed pointnonexpansive mappinguniformly convex space

MSC classification

Primary: 47H20: Semigroups of nonlinear operators
Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 47H10: Fixed-point theorems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 284 - 292
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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