Nonlinear ergodic theorems for an amenable semigroup of nonexpansive mappings in a Banach space
Norimichi Hirano, Wataru Takahashi · Pacific Journal of Mathematics · 1984
Let C be a nonempty closed convex subset of a Banach space, S a semigroup of nonexpansive mappings / of C into itself, and F(S) the set of common fixed points of mappings t.Then we deal with the existence of a nonexpansive retraction P of C onto F(S) such that Pt -tP -P for each t E S and Px is contained in the closure of the convex hull of {tx: t E S} for each x E C. That is, we prove nonlinear ergodic theorems for a semigroup of nonexpansive mappings in a Banach space.