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Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property

Volume 154 / 2018

Sławomir Borzdyński Colloquium Mathematicum 154 (2018), 157-165 MSC: Primary 47H10; Secondary 46B20, 47H09. DOI: 10.4064/cm7216-5-2017 Published online: 23 August 2018


Suppose that $E$ is a Banach space, $\tau $ a topology under which the norm of $E$ becomes $\tau $-lower semicontinuous and $\mathcal {S}$ a commuting family of $\tau $-continuous nonexpansive mappings defined on a $\tau $-compact convex subset $C$ of $E.$ It is shown that the set of common fixed points of $\mathcal {S}$ is a nonempty nonexpansive retract of $C$. Along the way, a few other related fixed point theorems are derived.


  • Sławomir BorzdyńskiInstitute of Mathematics
    Maria Curie-Skłodowska University
    20-031 Lublin, Poland

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