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COMMON FIXED POINTS FOR SEMIGROUPS OF POINTWISE LIPSCHITZIAN MAPPINGS IN BANACH SPACES

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  26 September 2011

W. M. KOZLOWSKI
W. M. KOZLOWSKI*
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia (email: w.m.kozlowski@unsw.edu.au)
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Abstract

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Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the existence of common fixed points for pointwise Lipschitzian semigroups of nonlinear mappings Tt:C→C, where each Tt is pointwise Lipschitzian. The latter means that there exists a family of functions αt:C→[0,∞) such that for x,y∈C. We also demonstrate how the asymptotic aspect of the pointwise Lipschitzian semigroups can be expressed in terms of the respective Fréchet derivatives.

Keywords

fixed pointcommon fixed pointLipschitzian mappingpointwise Lipschitzian mappingpointwise contractionssemigroup of mappingsasymptotic pointwise nonexpansive mappinguniformly convex Banach spacestochastic dynamical systems

MSC classification

Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 353 - 361
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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