Natural extension of Banach fixed point theorem
Abstract
This study aims to develop new versions of the Banach fixed-point theorem in generalized metric spaces endowed with a direct sum structure. Specifically, we assume a diagonal matrix A in Rd×d and establish more appropriate contraction conditions to improve the applicability of fixed point results within this framework. Since the condition that the matrix A must converge to zero is unnecessary, our approach yields stronger results than the Perov one. As an application of our findings, we examine the existence and uniqueness of solutions for a system of matrix equations. This version is more powerful than the Perov version. We introduced some examples and applications to illustrate our result.
Copyright © 2025 Saleh Omran, Ghadah Albeladi. 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
S. Omran, G. Albeladi, Natural extension of Banach fixed point theorem, Adv. Fixed Point Theory 15 (2025), 18. https://doi.org/10.28919/afpt/9260
BibTeX
@article{Omran2025,
author = {Omran, Saleh and Albeladi, Ghadah},
title = {Natural extension of Banach fixed point theorem},
journal = {Adv. Fixed Point Theory},
volume = {15},
year = {2025},
pages = {18},
doi = {10.28919/afpt/9260}
}