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arXiv · 1811.00792

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

Sławomir Borzdyński
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Abstract

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

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Sławomir Borzdyński. 2018-11-02. Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property. https://doi.org/10.4064/cm7216-5-2017

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