An ultrafilter approach to locally almost nonexpansive maps

Title: An ultrafilter approach to locally almost nonexpansive maps
Creator: Kirk, W. A.; Sims, Brailey
Relation: Nonlinear Analysis: Theory, Methods and Applications Vol. 63, Issue 5-7, p. e1241-e1251
Publisher Link: http://dx.doi.org/10.1016/j.na.2004.10.017
Publisher: Elsevier
Resource Type: journal article
Date: 2005
Description: Let K be a bounded closed convex subset of a Banach space X, and suppose f:K→K is 'locally almost nonexpansive' in the sense of Nussbaum. It is shown that the mapping Id-f is demiclosed if X is either uniformly convex or satisfies the Opial property. These facts are known, but the ultrapower approach given here is new. In fact, we give ultrapower characterizations of locally almost nonexpansive maps and of the Opial property. Finally, we obtain a new demiclosedness result for the class of 'locally almost pointwise contractive mappings'.
Subject: locally almost nonexpansive mappings; fixed points; demiclosedness; the Opial property; Banach space ultrapowers
Identifier: http://hdl.handle.net/1959.13/28846
Identifier: uon:2253
Identifier: ISSN:0362-546X
Language: eng
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