Fixed point approximation via a new faster iteration process in Banach spaces with an application

Nour-Eddine El Harmouchi, Rida Outass, Karim Chaira, Jamal Mouline

Abstract


In this paper, we propose a new iterative process for approximating fixed points of mappings. First, we prove that our iterative scheme is faster than the iterative processes of Thakur and Piri for contractive mapping in Banach spaces. To support the analytical results, we give some numerical examples using the software program MATLAB. Afterwards, we give some weak and strong convergence theorems for monotone generalized α-nonexpansive mapping in uniformly convex ordered Banach spaces. To justify the utility of our main results, we presented an application regarding the approximation of the solution to an integral equation, supported by an illustrative example.

Full Text: PDF

Published: 2024-01-02

How to Cite this Article:

Nour-Eddine El Harmouchi, Rida Outass, Karim Chaira, Jamal Mouline, Fixed point approximation via a new faster iteration process in Banach spaces with an application, Adv. Fixed Point Theory, 14 (2024), Article ID 2

Copyright © 2024 Nour-Eddine El Harmouchi, Rida Outass, Karim Chaira, Jamal Mouline. 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.

Advances in Fixed Point Theory

ISSN: 1927-6303

Editorial Office: [email protected]

Copyright ©2024 SCIK Publishing Corporation