Geodesic
Weak uniform normal structure and iterative fixed points of nonexpansive mappings
Colloquium Mathematicum, Tome 68 (1995) no. 1, pp. 17-23.

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This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
DOI : 10.4064/cm-68-1-17-23
Keywords: nonexpansive mapping, iterative fixed point, geometrical coefficients of Banach spaces, James' quasi-reflexive space, weak uniform normal structure

T. Domínguez Benavides 1 ; G. López Acedo 1 ; Hong Xu 1

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T. Domínguez Benavides; G. López Acedo; Hong Xu. Weak uniform normal structure and iterative fixed points of nonexpansive mappings. Colloquium Mathematicum, Tome 68 (1995) no. 1, pp. 17-23. doi : 10.4064/cm-68-1-17-23. http://geodesic.mathdoc.fr/articles/10.4064/cm-68-1-17-23/

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