Results on Rectangular G^b-Metric Space Endowed With Mann’s Iterative Scheme

This research presents a comprehensive investigation into the properties and applications of Mann’s iterative scheme within the specialized framework of convex rectangular G^b-metric space. The primary objective is to establish novel fixed point theorems under these conditions. A key advantage of employing Mann’s iterative scheme, as opposed to the more conventional Picard iteration, is its superior flexibility and significantly accelerated convergence rate, which enhances the efficiency of locating fixed points. To illustrate the real-world viability and robustness of our proposed approach, we provide a detailed illustrative example. Furthermore, the article is concluded by showcasing the direct applicability of these results and employing them to derive existence and uniqueness theorems for solutions to a class of integral equations. By advancing the theoretical foundations of fixed point theory in convex rectangular Gb^-metric spaces, this study not only contributes to the mathematical literature but also opens new avenues for applications in fields such as optimization and non-linear analysis, where iterative schemes play a crucial role.