Geodesic
A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings
Sławomir Borzdyński 1   ; Andrzej Wiśnicki 1
1 Department of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland
Studia Mathematica, Tome 225 (2014) no. 2, pp. 173-181 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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It is shown that if $\mathcal {S}$ is a commuting family of weak$^{\ast }$ continuous nonexpansive mappings acting on a weak$^{\ast }$ compact convex subset $C$ of the dual Banach space $E,$ then the set of common fixed points of $\mathcal {S}$ is a nonempty nonexpansive retract of $C$. This partially solves an open problem in metric fixed point theory in the case of commutative semigroups.
DOI : 10.4064/sm225-2-4
Keywords: shown mathcal commuting family weak ast continuous nonexpansive mappings acting weak ast compact convex subset dual banach space nbsp set common fixed points mathcal nonempty nonexpansive retract nbsp partially solves problem metric fixed point theory commutative semigroups

Sławomir Borzdyński  1   ; Andrzej Wiśnicki  1

1 Department of Mathematics Maria Curie-Skłodowska University 20-031 Lublin, Poland 
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Sławomir Borzdyński; Andrzej Wiśnicki. A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings. Studia Mathematica, Tome 225 (2014) no. 2, pp. 173-181. doi: 10.4064/sm225-2-4

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