New Best Proximity Point Results via Simulation Functions in Fuzzy Metric Spaces

Abdelhamid  Moussaoui; Choonkil Park; Said Melliani

doi:10.5269/bspm.65506

Abdelhamid Moussaoui Laboratory of Applied Mathematics \& Scientific Computing LMACS, Faculty of Sciences and Technics, Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco https://orcid.org/0000-0003-4897-1132
Choonkil Park Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
Said Melliani Laboratory of Applied Mathematics \& Scientific Computing LMACS, Faculty of Sciences and Technics, Sultan Moulay Slimane University, PO Box 523, 23000 Beni Mellal, Morocco

Résumé

In this paper, we introduce the concepts of $\mathcal{FZ}$-proximal contraction of type$-$I and type-II and prove some $g-$best proximity point results involving $\mathcal{FZ}$-simulation functions under suitable conditions on the framework of fuzzy metric spaces. Our results unify, generalize, and improve a lot of solid papers in the same context and may lay the groundwork for new directions of best proximity and fuzzy fixed point theory. Also, an example is given to support the theoretical results.

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