<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Department of Mathematical and Statistical Sciences

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Feb 23, 2019

Page range: 67 - 87

Received: May 05, 2018

Accepted: Aug 28, 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0007

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

© 2018 Anthony To-Ming Lau et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Feb 23, 2019

Page range: 67 - 87

Received: May 05, 2018

Accepted: Aug 28, 2018

DOI: https://doi.org/10.2478/aupcsm-2018-0007

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

© 2018 Anthony To-Ming Lau et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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