Common fixed point results for Boyd-Wong and Meir-Keeler contraction in F-Metric spaces

Abstract

A new notion of metric space generalization has been defined by Jleli and Samet, namely F-metric space, in 2018. The objective of this study is to prove the existence and uniqueness of a common fixed point in the context of F-metric space. We construct theorems of a common fixed point for commuting mapping pairs with Boyd-Wong and Meir-Keeler contraction in this space. Moreover, we extend the results of Park and Bae (1981) and Bera et al. (2022) to common fixed point theorems and F-metric space, respectively. The Boyd-Wong contraction is attractive to discuss since we cannot apply the metrizability result on the F-metric space to prove the theorem. The Meir-Keeler contraction is also interesting since it is a generalization of the Boyd-Wong contraction. Lastly, we provide an example of each case to support the findings of our study.