A nonlinear ergodic theorem for a reversible semigroup of nonexpansive mappings in a Hilbert space
Wataru Takahashi · Proceedings of the American Mathematical Society · 1986
Let C C be a nonempty closed convex subset of a Hilbert space, S S a right reversible semitopological semigroup, S = { T t : t ∈ S } \mathcal {S} = \{ {T_t}:t \in S\} a continuous representation of S S as nonexpansive mappings on a closed convex subset C C into C C , and F ( S ) F(\mathcal {S}) the set of common fixed points of mappings T t , t ∈ S {T_t},\;t \in S . Then we deal with the existence of a nonexpansive retraction P P of C C onto F ( S ) F(\mathcal {S}) such that P T t = T t P = P P{T_t} = {T_t}P = P for each