On AI-iteration process for finding fixed points of enriched contraction and enriched nonexpansive mappings with application to fractional BVPs
Abstract
In this article, we consider the AI-iteration process for approximating the fixed points of enriched contraction and enriched nonexpansive mappings. Firstly, we prove the strong convergence of the AI-iteration process to the fixed points of enriched contraction mappings. Furthermore, we present a numerical experiment to demonstrate the efficiency of the AI-iterative method over some existing methods. Secondly, we establish the weak and strong convergence results of AI-iteration method for enriched nonexpansive mappings in uniformly convex Banach spaces. Thirdly, the stability analysis results of the considered method is presented. Finally, we apply our results to the solution of fractional boundary value problems in Banach spaces.
Copyright © 2024 J. Oboyi, R. E. Orim, A. E. Ofem, A. Maharaj, O. K. Narain. 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
J. Oboyi, R. E. Orim, A. E. Ofem, A. Maharaj, O. K. Narain, On AI-iteration process for finding fixed points of enriched contraction and enriched nonexpansive mappings with application to fractional BVPs, Adv. Fixed Point Theory 14 (2024), 56. https://doi.org/10.28919/afpt/8812
BibTeX
@article{Oboyi2024,
author = {Oboyi, J. and Orim, R. E. and Ofem, A. E. and Maharaj, A. and Narain, O. K.},
title = {On AI-iteration process for finding fixed points of enriched contraction and enriched nonexpansive mappings with application to fractional BVPs},
journal = {Adv. Fixed Point Theory},
volume = {14},
year = {2024},
pages = {56},
doi = {10.28919/afpt/8812}
}