Abstract
Let C be a bounded, closed, convex subset of a uniformly convex metric space (M, d). In this paper, we introduce the concept of asymptotic pointwise nonexpansive semigroups of nonlinear mappings T-t : C -> C, i.e., a family such that T-0(x) = x, Ts+t = T-s(T-t(x)), and d(T-t(x), T-t(y)) <= alpha(t)(x)d(x, y), where lim sup(t ->infinity) alpha(t)(x) <= 1 for every x is an element of C. Then we investigate the existence of common fixed points for asymptotic pointwise nonexpansive semigroups. The proof is based on the concept of types extended to one parameter family of points.