On the weak-approximate fixed point property

被引：7

作者：

Barroso, Cleon S. ^{[1
]}

Lin, Pei-Kee ^{[2
]}

机构：

[1] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil

[2] Univ Memphis, Dept Math, Memphis, TN 38152 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 365卷 / 01期

关键词：

Weakly null sequences; Rosenthal's l(1)-theorem; Fixed point property; Asymptotic approximation; Weak topology; THEOREMS; SPACES;

D O I：

10.1016/j.jmaa.2009.10.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a Banach space and C a bounded, closed, convex subset of X, C is said to have the weak-approximate fixed point property if for any norm-continuous mapping f : C -> C, there exists a sequence {x(n)} in C such that (x(n) - f (x(n)))(n) converges to 0 weakly. It is known that every infinite-dimensional Banach space with the Schur property does not have the weak-approximate fixed point property. In this article. we show that every Asplund space has the weak-approximate fixed point property. Applications to the asymptotic fixed point theory are given. (c) 2009 Elsevier Inc. All rights reserved.

引用

页码：171 / 175

页数：5

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