An ultrafilter approach to locally almost nonexpansive maps

Kirk, W. A. and Sims, Brailey (2005) An ultrafilter approach to locally almost nonexpansive maps. Nonlinear Analysis: Theory . -.

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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'.

Item Type: Article
Uncontrolled Keywords: locally almost nonexpansive mappings, fixed points, demiclosedness, the Opial property, Banach space ultrapowers
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 28 Sep 2012 12:05

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