Asymptotic behavior for almost-orbits of asymptotically nonexpansive type mappings in a metric space

摘要

Let (M, rho) be a metric space and tau a Hausdorff topology on M such that {M,tau} is sequentially compact. Let T be a rho-asymptotically nonexpansive type self-mapping of M and u = {x(n)} a rho-bounded almost-orbit of T. We study the tau-convergence of u in M when the triplet {M, p, tau} satisfies various types of tau-Opial conditions. Our results, which also hold for the continuous case of one-parameter semigroups, extend and unify many previously known results [ 1, 5, 9, 10, 1.2-19, 21, 22], and answers affirmatively an open question of S. Reich [20, p.550] in the very general context of a metric space.