Some fixed point theorems in 1-M-complete fuzzy metric-like spaces

Abstract

Very recently, in order to unify the notions of fuzzy metric space and metric-like space, Shukla and Abbas introduced the concept of fuzzy metric-like space and proved some fixed-point results in this setting. In this article, we modify the notion of Cauchy sequence and completeness to generalize their results. Thus, we extend their theorems to a more general framework, which is also appropriate to generalize some recent, well-known results in this line of research. Furthermore, several examples are presented to illustrate the significance of our results.

Keywords:

• 1-M-complete fuzzy metric-like spaces
• 1-M-Cauchy sequence
• $\mathcal{B}$-contraction
• fixed point

Acknowledgements

The authors thank Editor-in-Chief and Referee(s) for their valuable comments and suggestions, which were very useful to improve the presentation of the paper. S. Shukla is thankful to Professor M.K. Dube for his regular encouragements and motivation for research. A.F. Roldán-López-de-Hierro is grateful to the Department of Quantitative Methods for Economics and Business of the University of Granada.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE.