Year: 2025
Type: article
Abstract: This paper investigates fixed-point theorems within \( MR \)-metric spaces, an extension of standard metric spaces, emphasizing the existence and uniqueness of fixed points for continuous mappings \( S: \mathbb{X} \to \mathbb{X} \), where \( \mathbb{X} \) is a closed, bounded, and convex subset of a Banach space \( (E, \|\cdot\|) \). The study establishes that if \( S \) satisfies a contractive condition involving the \( MR \)-metric with a constant \( k \in [0, 1) \), and a measure of noncompactness condition governed by a function \( \phi \) where \( \phi(t) < t \) for \( t > 0 \), then \( S \) possesses a unique fixed point \( \upsilon^* \). The findings have significant applications in solving nonlinear integral equations, ensuring stability of iterative processes, optimization, game theory, economic equilibria, and boundary value problems, showcasing the versatility of \( MR \)-metric spaces in addressing noncompact settings and fixed-point problems.
Author: Abed Al-Rahman Malkawi
Institution: Amman Arab University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410004653