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1998 The $\tau$-fixed point property for nonexpansive mappings
Tomás Domínguez Benavides, jesús García Falset, Maria A. Japón Pineda
Abstr. Appl. Anal. 3(3-4): 343-362 (1998). DOI: 10.1155/S1085337598000591


Let X be a Banach space and τ a topology on X. We say that X has the τ-fixed point property (τ-FPP) if every nonexpansive mapping T defined from a bounded convex τ-sequentially compact subset C of X into C has a fixed point. When τ satisfies certain regularity conditions, we show that normal structure assures the τ-FPP and Goebel-Karlovitz′s Lemma still holds. We use this results to study two geometrical properties which imply the τ-FPP: the τ-GGLD and M(τ) properties. We show several examples of spaces and topologies where these results can be applied, specially the topology of convergence locally in measure in Lebesgue spaces. In the second part we study the preservence of the τ-FPP under isomorphisms. In order to do that we study some geometric constants for a Banach space X such that the τ-FPP is shared by any isomorphic Banach space Y satisfying that the Banach-Mazur distance between X and Y is less than some of these constants.


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Tomás Domínguez Benavides. jesús García Falset. Maria A. Japón Pineda. "The $\tau$-fixed point property for nonexpansive mappings." Abstr. Appl. Anal. 3 (3-4) 343 - 362, 1998.


Published: 1998
First available in Project Euclid: 8 April 2003

zbMATH: 0971.47035
MathSciNet: MR1749415
Digital Object Identifier: 10.1155/S1085337598000591

Primary: 47H09 , 47H10

Keywords: asymptotically regular mappings , fixed point , ‎Lebesgue spaces , local convergence in measure , Nonexpansive mapping , stability of the fixed point property , uniformly Lipschitzian mappings

Rights: Copyright © 1998 Hindawi

Vol.3 • No. 3-4 • 1998
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