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

Anthony To-Ming Lau; Yong Zhang

doi:10.2478/aupcsm-2018-0007

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

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Volume 17 (2018): Issue 1 (December 2018)

By: Anthony To-Ming Lau and Yong Zhang

Open Access

|Feb 2019

Abstract

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.

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Articles in this issue

DOI: https://doi.org/10.2478/aupcsm-2018-0007 | Journal eISSN: 2300-133X | Journal ISSN: 2081-545X

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Language: English

Page range: 67 - 87

Submitted on: May 5, 2018

Accepted on: Aug 28, 2018

Published on: Feb 23, 2019

Published by: Pedagogical University of Cracow

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

amenability,

semigroups,

non-expansive mappings,

weak*-compact convex sets,

Related subjects:

© 2019 Anthony To-Ming Lau, Yong Zhang, published by Pedagogical University of Cracow
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 17 (2018): Issue 1 (December 2018)