Convergence analysis of Picard-Abbas hybrid iterative process
Abstract
Iterative methods play a crucial role in numerical analysis and optimization problems. This paper introduces a hybrid fixed-point iterative process and compares its convergence rate with the established Abbas iterative approach, using Berinde’s criteria. Additionally, the stability and data dependency of the improved iterative process are established. This study’s purpose is to demonstrate the superiority, in terms of convergence speed, of the hybrid approach and provide further insights into its stability and data dependency. Furthermore, we apply the iterative process to find solutions of delay differential equations.
Copyright © 2024 Manbhalang Chyne, Naveen Kumar. 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
M. Chyne, N. Kumar, Convergence analysis of Picard-Abbas hybrid iterative process, Adv. Fixed Point Theory 14 (2024), 21. https://doi.org/10.28919/afpt/8552
BibTeX
@article{Chyne2024,
author = {Chyne, Manbhalang and Kumar, Naveen},
title = {Convergence analysis of Picard-Abbas hybrid iterative process},
journal = {Adv. Fixed Point Theory},
volume = {14},
year = {2024},
pages = {21},
doi = {10.28919/afpt/8552}
}