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.
Advances in Fixed Point Theory
ISSN: 1927-6303
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