It is shown that if 𝓢 is a commuting family of weak* continuous nonexpansive mappings acting on a weak* compact convex subset C of the dual Banach space E, then the set of common fixed points of 𝓢 is a nonempty nonexpansive retract of C. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-4,
author = {S\l awomir Borzdy\'nski and Andrzej Wi\'snicki},
title = {A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {173-181},
zbl = {1316.47046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-4}
}
Sławomir Borzdyński; Andrzej Wiśnicki. A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings. Studia Mathematica, Tome 223 (2014) pp. 173-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm225-2-4/