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

Abstract

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 I={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 I . 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.