Fixed-Point Theorems in Fuzzy Metric Spaces via Fuzzy F-Contraction

Huaping Huang,Mirjana Brdar,Tatjana Došenović,Biljana Carić,Dušan Rakić

doi:10.3390/math9060641

Huaping Huang, Mirjana Brdar + Show 3 more

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https://doi.org/10.3390/math9060641

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Abstract

The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature.

Highlights

Introduction and PreliminariesBased on the theory of fuzzy sets introduced by Zadeh [1], George and Veeramani [2], provided axioms to fuzzy metric spaces
By applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature
One of the most interesting motivations is the fixed-point theory established in fuzzy metric spaces, which was initiated by Grabiec [5], where a fuzzy metric version of the Banach contraction principle was presented

Summary

Introduction

Introduction and PreliminariesBased on the theory of fuzzy sets introduced by Zadeh [1], George and Veeramani [2], provided axioms to fuzzy metric spaces. We cope with fixed-point theorems for fuzzy F-contraction in the setting of fuzzy metric spaces. Utilizing the lemma mentioned above, we obtain some fixed-point theorems for fuzzy F-contraction with shorter conditions and straightforward proofs.

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Conclusion