Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

被引：6

作者：

Lau, Anthony To-Ming ^{[1
]}

Zhang, Yong ^{[2
]}

机构：

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

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

来源：

ANNALES UNIVERSITATIS PAEDAGOGICAE CRACOVIENSIS-STUDIA MATHEMATICA | 2018年 / 17卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

amenability; semigroups; non-expansive mappings; weak*-compact convex sets; common fixed point; invariant mean; submean;

D O I：

10.2478/aupcsm-2018-0007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach space as weak* continuous and norm nonexpansive mappings. Our investigation in the paper centers around this problem. Our main results rely on the well-known Ky Fan's inequality for convex functions.

引用

页码：67 / 87

页数：21

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