A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings

Sławomir Borzdyński, and Andrzej Wiśnicki. "A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings." Studia Mathematica 225.2 (2014): 173-181. <http://eudml.org/doc/286671>.

@article{SławomirBorzdyński2014,
abstract = {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.},
author = {Sławomir Borzdyński, Andrzej Wiśnicki},
journal = {Studia Mathematica},
keywords = {fixed point property; nonexpansive mapping; weak topologies; commuting mappings; nonexpansive retract},
language = {eng},
number = {2},
pages = {173-181},
title = {A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings},
url = {http://eudml.org/doc/286671},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Sławomir Borzdyński
AU - Andrzej Wiśnicki
TI - A common fixed point theorem for a commuting family of weak* continuous nonexpansive mappings
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 2
SP - 173
EP - 181
AB - 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.
LA - eng
KW - fixed point property; nonexpansive mapping; weak topologies; commuting mappings; nonexpansive retract
UR - http://eudml.org/doc/286671
ER -