Properties of fixed-point sets of nonexpansive mappings in Banach spaces
Properties of fixed-point sets of nonexpansive mappings in Banach spaces
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DOI：
10.1090/s0002-9947-1973-0324491-8
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发表时间：
1973-05
影响因子：
1.3
通讯作者：
Ronald E. Bruck
中科院分区：
文献类型：
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作者：
Ronald E. Bruck
设\(C\)是巴拿赫空间\(X\)的一个闭凸子集。\(C\)的子集\(F\)如果\(F = \varnothing\)或者存在从\(C\)到\(F\)的一个回缩且该回缩是一个非扩张映射，那么\(F\)就被称为\(C\)的一个非扩张回缩。本文的主要定理是：如果\(T : C \to C\)是非扩张的并且满足一个条件不动点性质，那么\(T\)的不动点集是\(C\)的一个非扩张回缩。这个结果被用于推广贝卢切（Belluce）和柯克（Kirk）关于一个有限的交换非扩张映射族存在公共不动点的一个定理。
. Let C be a closed convex subset of the Banach space X. A subset F of C is called a nonexpansive retract of C if either F = 0 or there exists a retraction of C onto F which is a nonexpansive mapping. The main theorem of this paper is that if T : C -» C is nonexpansive and satisfies a conditional fixed point property, then the fixed-point set of T is a nonexpansive retract of C. This result is used to generalize a theorem of Belluce and Kirk on the existence of a common fixed point of a finite family of commuting nonexpansive mappings.