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## Weak uniform normal structure and iterative fixed points of nonexpansive mappings

### Tom 68 / 1995

Colloquium Mathematicum 68 (1995), 17-23 DOI: 10.4064/cm-68-1-17-23

#### Streszczenie

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.

#### Autorzy

• T. Domínguez Benavides
• G. López Acedo
• Hong Xu

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