Abstract and Applied Analysis

The $\tau$-fixed point property for nonexpansive mappings

Tomás Domínguez Benavides, jesús García Falset, and Maria A. Japón Pineda

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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.

Article information

Abstr. Appl. Anal., Volume 3, Number 3-4 (1998), 343-362.

First available in Project Euclid: 8 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10

Fixed point nonexpansive mapping stability of the fixed point property uniformly Lipschitzian mappings asymptotically regular mappings local convergence in measure Lebesgue spaces


Benavides, Tomás Domínguez; Falset, jesús García; Japón Pineda, Maria A. The $\tau$-fixed point property for nonexpansive mappings. Abstr. Appl. Anal. 3 (1998), no. 3-4, 343--362. doi:10.1155/S1085337598000591. https://projecteuclid.org/euclid.aaa/1049832730

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