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

Sławomir Borzdyński; Andrzej Wiśnicki

Studia Mathematica (2014)

- Volume: 225, Issue: 2, page 173-181
- ISSN: 0039-3223

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topSławomir 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 -

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