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

Abstract

It is shown that if $S$ 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 $S$ is a nonempty nonexpansive retract of $C$. This partially solves a long-standing open problem in metric fixed point theory in the case of commutative semigroups.

Cited by in corpus (1)

• Applications of uniform asymptotic regularity to fixed point theorems