Convergence theorems and stability results of a two-step iteration scheme for pointwise asymptotically nonexpansive self mappings and pointwise asymptotically nonexpansive nonself mappings in uniformly convex Banach spaces

Abstract

We propose a two-step generalised lshikawa iteration scheme of hybrid mixed-type for two pointwise asymptotically nonexpansive self mappings and two pointwise asymptotically nonexpansive nonself mappings. Under the condition that pointwise asymptotically nonexpansive self mappings and pointwise asymptotically nonexpansive nonself mappings are compact, we proved demiclosedness principle for pointwise asymptotically nonexpansive nonself mappings; in addition, we established stability results and weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results modify, improve and generalise numerous results currently existing in literature.