APPROXIMATING COMMON FIXED POINTS OF NONEXPANSIVE SEMIGROUPS IN BANACH SPACES
Gang Eun Kim, Wataru Takahashi, Received August · Scientiae mathematicae Japonicae · 2005
In this paper, we prove the following theorem: Let C be a nonempty closed convex subset of a uniformly convex Banach space E whose norm is uniformly Gateaux differentiable, let � = {T (t ): t ≥ 0} be a strongly continuous semigroup of nonexpansive mappings on C such that F (� )= t≥0 F (T (t)) � ∅ and let P be the sunny nonexpansive retraction from C onto F (� ). For some u ∈ C, define a sequence {xn} in C by xn =( 1− αn)T (tn)xn + αnu, where 0 0 for all n ≥ 1 and lim n→∞ tn = lim n→∞ αn tn = 0. Then {xn} converges strongly to Pu .