ArticleOriginal scientific text
Title
Weak uniform normal structure and iterative fixed points of nonexpansive mappings
Authors 1, 1, 1
Affiliations
- Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain
Abstract
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.
Keywords
nonexpansive mapping, iterative fixed point, geometrical coefficients of Banach spaces, James' quasi-reflexive space, weak uniform normal structure
Bibliography
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Pages:
17-23
Main language of publication
English
Received
1994-01-03
Published
1995
Exact and natural sciences