The Fibonacci-Mann process for monotone total asymptotically nonexpansive mappings

Abstract

We study the existence and convergence of fixed points for monotone total asymptotically nonexpansive self-mappings in partially ordered Banach spaces. We generalize and improve several known results, including those of Rashwan et al, as well as the works of Alfuraidan and Khamsi for monotone asymptotically nonexpansive mappings and those of Schu on asymptotically nonexpansive mappings, extending them to the broader class of monotone total asymptotically nonexpansive mappings using the Fibonacci-Mann iteration process in a uniformly convex Banach space.