Demiclosedness principle and asymptotic behavior for nonexpansive mappings in metric spaces Original Research Article

Let (M, ρ) be a metric space, τ be a Hausdorff topology on M such that (M, ρ, τ) has Opialʹs condition, and T : M ↦ M be a nonexpansive mapping. Then for any ρ-bounded sequence {xn}, the condition {Tmxn} is τ-convergent to x for all m ϵ View the MathML source implies that Tx = x. This τ-demiclosedness principle is to be used to study the asymptotic behavior for almost-orbits of nonexpansive mappings and semigroups.