Fixed point theorem for nonexpansive semigroup on Banach space
Wataru Takahashi, Doo-Hoan Jeong · Proceedings of the American Mathematical Society · 1994
Let C be a nonempty closed convex subset of a uniformly convex Banach space, and let S be a semitopological semigroup such that RUC ( S ) {\text {RUC}}(S) has a left invariant submean. Then we prove a fixed point theorem for a continuous representation of S as nonexpansive mappings on C .