Best Proximity Point Results in Neutrosophic Fuzzy Metric Space for Ciric type α-ψ proximal contractive mappings

Samriddhi Ghosh; Ramakant Bhardwaj; Purvee Bhardwaj; Sneha Khandait; Satyendra Narayan

Authors

Samriddhi Ghosh Department of Mathematics, Amity University Kolkata, India;
Ramakant Bhardwaj 2Department of Mathematics, Amity University Kolkata, India;
Purvee Bhardwaj Department of Physics, JNCT Professional University, India;
Sneha Khandait Department of Science and Humanities, Thakur College of Engineering and Tecnology, India;
Satyendra Narayan School of Computer Science and Technology, Algoma University, Canada;

Keywords:

Neutrosophic sets (NS); Neutrosophic fuzzy sets (NFS); Continuous t-norm (CTN); Continuous t conorm (CTCN); Neutrosophic fuzzy metric space (NFMS); Best proximity point (BPP); α-proximal admissible (α-PA); α-ψ-proximal contractive (α-ψ-PCV ); α-ψ-contractive (α-ψ-CV ); t-uniformly continuous (t-unif. cont.); α admissible (α adm).

Abstract

The present manuscript delves into the ideology of best proximity point under the purview of
neutrosophic fuzzy metric space. For this purpose, the concept of a new type of mapping named α-proximal
admissible mapping has been defined under the realm of the said space. Also for the contractive condition,
the pre-existent ideologies of Ciric and rational contraction has been combined. Notably, for the sake of best
proximity, concept of α-ψ proximal contraction has also been considered. Here α and ψ can also be regarded as
control functions. Additionally, some examples and applications are also deduced in support of the established
results, for some particular conditions. To the best of known literatures, the results are established for the first
time in the mentioned area.

DOI 10.5281/zenodo.19103495.