  Suppose that Q is a family of seminorms on a locally convex space E which
determines the topology of E. We study the existence of Q-nonexpansive
retractions for families of Q-nonexpansive mappings and prove that a separated
and sequentially complete locally convex space $E$ that has the weak fixed
point property, has the weak fixed point property for commuting separable
semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's
problem [5] for locally convex spaces. Moreover, we prove the existence of
Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups.
