Fixed point properties for semigroups of nonlinear mappings on unbounded sets

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Lau, Anthony To-Ming¹  Zhang, Yong² 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Univ Manitoba, Dept Math, Winnipeg, MB R3T 2N2, Canada

关键词: Semigroup;    Fixed point;    Nonexpansive mappings;    Hilbert space;    Invariant mean;    Attractive point;   

DOI  :  10.1016/j.jmaa.2015.08.044

来源: Elsevier

【 摘 要 】

A well-known result of W. Ray asserts that if C is an unbounded convex subset of a Hilbert space, then there is a nonexpansive mapping T: C -> C that has no fixed point. In this paper we establish some common fixed point properties for a semitopological semigroup S of nonexpansive mappings acting on a closed convex subset C of a Hilbert space, assuming that there is a point c is an element of C with a bounded orbit and assuming that certain subspace of C-b(5) has a left invariant mean. Left invariant mean (or amenability) is an important notion in harmonic analysis of semigroups and groups introduced by von Neumann in 1929 [28] and formalized by Day in 1957 [5]. In our investigation we use the notion of common attractive points introduced recently by S. Atsushiba and W. Takahashi. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free