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.
Copyright © 2022 Imo Kalu Agwu, Donatus Ikechi Igbokwe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
I. K. Agwu, D. I. Igbokwe, 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, Adv. Fixed Point Theory 12 (2022), 8. https://doi.org/10.28919/afpt/7320
BibTeX
@article{Agwu2022,
author = {Agwu, Imo Kalu and Igbokwe, Donatus Ikechi},
title = {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},
journal = {Adv. Fixed Point Theory},
volume = {12},
year = {2022},
pages = {8},
doi = {10.28919/afpt/7320}
}