Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let C be a nonempty closed convex subset of a uniformly convex Banach space E with a Fréchet differentiable norm, G a right reversible semitopological semigroup, and 𝒮 = { S ( t ) : t ∈ G } a continuous representation of G as mappings of asymptotically nonexpansive type of C into itself. The weak convergence of an almost-orbit { u ( t ) : t ∈ G } of 𝒮 = { S ( t ) : t ∈ G } on C is established. Furthermore, it is shown that if P is the metric projection of E onto set F ( S ) of all common fixed points of 𝒮 = { S ( t ) : t ∈ G } , then the strong limit of the net { P u ( t ) : t ∈ G } exists.