A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings
Volume 225 / 2014
Studia Mathematica 225 (2014), 173-181
MSC: Primary 47H10; Secondary 46B20, 47H09.
DOI: 10.4064/sm225-2-4
Abstract
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.
