Fixed Point Theorems in the Fuzzy Supermetric Spaces and Application

Solomon Zerfu Degefa; Vizender Singh; Yohannes Gebru Aemro

doi:10.58715/bangmodjmcs.2025.11.13

Authors

Solomon Zerfu Degefa Research Scholar, Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, India
Vizender Singh Department of Mathematics, Guru Jambheshwar University of Science & Technology, Hisar, Haryana, India
Yohannes Gebru Aemro Department of Mathematics, Wolkite University, Wolkite, Ethiopia

DOI:

https://doi.org/10.58715/bangmodjmcs.2025.11.13

Keywords:

Fixed Point, Contractive Mappings, Supermetric Spaces, Fuzzy Supermetric Spaces, Fuzzy Metric Spaces, Fredholm Integral Equation

Abstract

This article introduces a new mathematical concept that extends the notion of a supermetric space, termed a fuzzy supermetric space. An illustrative example is provided to validate the proposed concept, and a class of contractive mappings is developed and employed to establish the existence and uniqueness of fixed-point theorems within the framework of fuzzy supermetric spaces. These results generalize both classical and recent findings as special cases within a broader, more inclusive setting, offering a more suitable framework for modeling and solving real-world problems. In addition, the concept of \((\beta{-}\theta)\)-contractive mappings is examined in this context. Finally, the theoretical results are applied to demonstrate the existence of a solution to the Fredholm integral equation.