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Fixed point results in b-Fuzzy metric spaces via pair upper (F, h)-class functions and αβ-contractive mappings

A.H. Ansari1, S.H.Jafari Petroudi1, T. Hamaizia2
1Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
2System Dynamics and Control Laboratory, Department of Mathematics and Informatics, OEB University, Algeria
Copyright © A.H. Ansari, S.H.Jafari Petroudi, T. Hamaizia. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This article proposes a new extension of fixed-point theorems in the context of b-fuzzy metric spaces based on Geraghty-type inequalities. We present the concept of pair upper \((F,h)\)-class functions, which play a key role in establishing existence and uniqueness of fixed points for contractive situations. These outcomes extend and generalize some eminent fixed-point theorems in fuzzy and b-metric spaces. We support our results by proper example.

Keywords: fixed point, Fuzzy metric spaces, completeness of fuzzy metric