This is an announcement for the paper "A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings" by Slawomir Borzdynski and Andrzej Wisnicki.
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.
Archive classification: math.FA
Submitted from: awisnic@hektor.umcs.lublin.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1407.0359
or