Improved Coincidence and Common Fixed Point Results in S-Metric Spaces via Simulation Functions

Abstract

One of the primary subjects of nonlinear analytical research is fixed-point theory. This is partly due to the fact that fixed-point theory is often the fundamental mathematical method used to demonstrate the existence of solutions to problems that naturally arise in applications. In addition to Definition the Picard sequence and Ȥ-s-contraction in S-metric space, we will talk about some remarks regarding the fixed-point theorem in S-metric space. The concept of a simulation function in S-metric space will be covered. In order to demonstrate the existence and uniqueness of coincidence fixed points in S-metric space, we will first introduce the idea of commuting mapping and then apply it to the commuting theorem in S-metric space. Remark and improvement to present fixed point result in d-metric space are provided. Many established fixed-point theories in the literature have been expanded and improved by relaxing traditional contraction assumptions and generalizing existing frameworks, based on our findings. Our results contribute to the ongoing development of fixed-point theories in generalized metric structures and provide a flexible approach for future research in these spaces.