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Weak uniform normal structure and iterative fixed points of nonexpansive mappings

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Domínguez Benavides T., López Acedo G., Xu H.-K.

Colloquium Mathematicum

1995

tom 68

nr 1

17-23

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Domínguez Benavides T.

1 López Acedo G.

1 Xu H.-K.

1 1995

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Weak uniform normal structure and iterative fixed points of nonexpansive mappings