A COMMON FIXED POINT THEOREM FOR A COMMUTING FAMILY OF NONEXPANSIVE MAPPINGS
A COMMON FIXED POINT THEOREM FOR A COMMUTING FAMILY OF NONEXPANSIVE MAPPINGS
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非扩张映射通勤族的公共不动点定理
DOI：
10.2140/pjm.1974.53.59
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发表时间：
1974
影响因子：
0.6
通讯作者：
Ronald E. Bruck
中科院分区：
文献类型：
--
作者：
Ronald E. Bruck
证明了如果Banach空间的闭凸子集C同时具有非扩张映象的不动点性质和条件不动点性质，且C是弱紧的或有界可分的，则C的任何交换族的非扩张自映象都有一个公共不动点.公共不动点集是C的非扩张收缩。
It is shown that if a closed convex subset C of a Banach space has both the fixed point property and the conditional fixed point property for nonexpansive mappings and C is either weakly compact or bounded and separable, then any commuting family of nonexpansive self-mappings of C has a common fixed point. The set of common fixed points is a nonexpansive retract of C.