Some Generalized Fixed Point and Common Fixed Point Theorems in S-Metric Spaces

Yashpal, Rishikant Agnihotri

Abstract: This article delves into the realm of S-metric spaces, an extension of metric spaces, exploring their fundamental properties and applications in fixed point theory. Beginning with a historical overview of key fixed point theorems and their limitations, the paper introduces the concept of S-metric spaces and provides definitions for essential terms. The main focus lies on establishing several fixed point theorems and common fixed points in complete S-metric spaces. The theorems presented here provide not only the existence of fixed points but also uniqueness, contributing to a deeper understanding of these spaces and their applications. The article combines theoretical explanations with rigorous proofs, making it a valuable resource for researchers and practitioners in functional analysis and topology.

Keywords: Fixed point, common fixed point, contractive mappings, S-metric space