  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.
