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A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings

Tom 225 / 2014

Sławomir Borzdyński, Andrzej Wiśnicki Studia Mathematica 225 (2014), 173-181 MSC: Primary 47H10; Secondary 46B20, 47H09. DOI: 10.4064/sm225-2-4

Streszczenie

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.

Autorzy

  • Sławomir BorzdyńskiDepartment of Mathematics
    Maria Curie-Skłodowska University
    20-031 Lublin, Poland
    e-mail
  • Andrzej WiśnickiDepartment of Mathematics
    Maria Curie-Skłodowska University
    20-031 Lublin, Poland
    e-mail

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