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.
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页码：1562 / 1571
页数：10
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