Nonexpansive, ๐ฏ-continuous antirepresentations have common fixed points
Wojciech Bartoszek ยท Proceedings of the American Mathematical Society ยท 1999
Let C C be a closed convex subset of a Banach (dual Banach) space X \mathfrak {X} . By S \mathcal {S} we denote an antirepresentation { T s : s โ S } \{ T_{s} \,:\, s \in S \} of a semitopological semigroup S S as nonexpansive mappings on C C . Suppose that the mapping S ร C โ ( s , x ) โ T s x โ C S \times C i (s,x) \to T_{s}x \in C is jointly continuous when C C has the weak (weak*) topology and the Banach space R U C ( S ) RUC(S) of bounded right uniformly continuous functions on S S has a right invariant mean. If C C is weakly compact (for some x โ C x \in C the set