Abstract :
Let G be a semitopological semigroup. Let C be a closed convex subset of a
uniformly convex Banach space E with a Fr´echet differentiable norm and Ts
Tt : tgG4be a continuous representation of G as asymptotically nonexpansive
type mappings of C into itself such that the common fixed point set F T. of T.
in C is nonempty. We prove in this paper that if G is right reversible, then for
every almost-orbit u ?. of T, FsgG co u t. : tGs4lF T. consists of at most one
point. Further, FsgGco Ttx : tGs4lF T. is nonempty for each xgC if and
only if there exists a nonexpansive retraction P of C onto F T. such that
PTssTsPsP for all sgG and P x. is in the closed convex hull of Tsx : sgG4,
xgC. This result is applied to study the problem of weak convergence of the net
u t.: tgG4 to a common fixed point of T
