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

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