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

Sławomir Borzdyński, Andrzej Wiśnicki (2014)

Studia Mathematica

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.

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