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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/28846

Title

An ultrafilter approach to locally almost nonexpansive maps

Author/Creator

Kirk, W. A.;  Sims, Brailey

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'.

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

Date

2005

Publisher

Elsevier

Keyword(s)

locally almost nonexpansive mappings;  fixed points;  demiclosedness;  the Opial property;  Banach space ultrapowers

Resource Type

journal article

Identifier

http://hdl.handle.net/1959.13/28846

Identifier

ISSN:0362-546X

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Subject

"Nonlinear Analysis: Theory, Methods and Applications"

 

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