Asymptotic behavior for almost-orbits of a reversible semigroup of non-Lipschitzian mappings in a metric space

Let (M, p) be a metric space and tau a Hausdorff topology on M such that {M, tau} is compact. Let S be a right reversible semitopological semigroup and G = {T(s): s is an element of S} a representation of S as rho-asymptotically nonexpansive type self-mappings of M and u a rho-bounded almost-orbit of G. We study the tau-convergence of the net {u(s): s is an element of S} in M when the triplet {M, p, tau} satisfies various types of tau-Opial conditions. Our results extend and unify many previously known results. (C) 2002 Elsevier Science (USA). All rights reserved.