Fixed point properties and proximinality in Banach spaces

被引：5

作者：

Dominguez Benavides, T. ^{[1
]}

Garcia Falset, J. ^{[2
]}

Llorens-Fuster, E. ^{[2
]}

Lorenzo Ramirez, P. ^{[1
]}

机构：

[1] Univ Seville, Dept Anal Matemat, E-41080 Seville, Spain

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 5-6期

关键词：

Fixed points; Nonexpansive mappings; Mappings admitting a center; Weak star topology; SETS; EQUIVALENT; MAPPINGS;

D O I：

10.1016/j.na.2008.12.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the existence of a fixed point for several classes of mappings (mappings admitting a center, nonexpansive mappings, asymptotically nonexpansive mappings) defined on the closed convex subsets of a Banach space satisfying some proximinality conditions. In particular, we derive a sufficient condition, more general than weak star compactness, such that if C is a bounded closed convex subset of l(1) satisfying this condition, then every nonexpansive mapping T : C -> C has a fixed point. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：1562 / 1571

页数：10

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