Fuzzy Fixed Point Results in F-Metric Spaces with Applications

Monairah Alansari,Akbar Azam,Shehu Shagari Mohammed

doi:10.1155/2020/5142815

Abstract

In this paper, some concepts of F-metric spaces are used to study a few fuzzy fixed point theorems. Consequently, corresponding fixed point theorems of multivalued and single-valued mappings are discussed. Moreover, one of our obtained results is applied to establish some conditions for existence of solutions of fuzzy Cauchy problems. It is hoped that the established ideas in this work will awake new research directions in fuzzy fixed point theory and related hybrid models in the framework of F-metric spaces.

Highlights

One of the challenges in mathematical modeling of practical phenomena relates to the indeterminacy induced by our inability to categorize events with adequate precision
The concept of fuzzy set was initiated by Zadeh [1] in 1965 as one of the uncertainty approaches to construct mathematical models compatible with real world problems in engineering, life science, economics, medicine, language theory, and so on
The notion of fixed point results for fuzzy set-valued mappings and fuzzy contractions was initiated by Heilpern [2] who proved a fixed point theorem parallel to the Banach fixed point theorem in the frame of fuzzy set

Summary

Introduction

One of the challenges in mathematical modeling of practical phenomena relates to the indeterminacy induced by our inability to categorize events with adequate precision. The concept of fuzzy set was initiated by Zadeh [1] in 1965 as one of the uncertainty approaches to construct mathematical models compatible with real world problems in engineering, life science, economics, medicine, language theory, and so on. The basic ideas of fuzzy set have been extended in different directions. Thereafter, several authors have studied and applied fuzzy fixed point results in different settings [4, 5], see, for example [6,7,8,9,10,11,12,13,14] and the references therein

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Conclusion