New Contraction Principle in Revised Fuzzy k-Metric Spaces

Introduction Metric spaces play a crucial role in mathematical analysis and topology. In recent years, fuzzy metric spaces have been widely studied due to their applications in various fields. Alexander Sostak introduced the concept of revised fuzzy metric spaces, which extends traditional fuzzy metric spaces by incorporating revised fuzzy sets. In this paper, we introduce a further generalization called revised fuzzy metric spaces, which allows for the involvement of multiple parameters (), thereby enhancing the flexibility and applicability of the framework. Objectives The primary aim of this study is to define and explore the fundamental properties of revised fuzzy metric spaces. We investigate their topological structure and establish significant properties such as first countability and the Hausdorff condition. Additionally, we extend existing results in the literature by proving a fixed-point theorem in this new setting. Method We begin by formally defining a revised fuzzy k-metric space and developing its basic properties. Using topological arguments, we demonstrate that the topology induced by a revised fuzzy metric is first countable and that the space satisfies the Hausdorff condition. Finally, we extend the fixed-point theorem established by Muraliraj and Thangathamizh into the context of revised fuzzy metric spaces, using analytical and set-theoretic techniques. Result Our findings confirm that revised fuzzy k-metric spaces preserve essential topological characteristics such as first countability and Hausdorff separation. Furthermore, the fixed-point theorem proved in this study generalizes previous results and demonstrates the broader applicability of revised fuzzy metric spaces in fixed-point theory. Conclusion This study introduces revised fuzzy metric spaces as a generalization of revised fuzzy metric spaces, providing a more comprehensive framework for analyzing metric structures with multiple parameters. The established topological properties and fixed-point theorem contribute to the further development of fuzzy metric theory, opening new avenues for future research in mathematical analysis and its applications.