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Research Article | Open Access

A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces

Khalil Javed1( ), Muhammad Nazam2( ), Fahad Jahangeer1, Muhammad Arshad1, Manuel De La Sen3
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan
Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad, Pakistan
Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country (UPV/EHU) Campus of Leioa, 48940-Leioa Bizkaia, Spain
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Abstract

We introduce a new type of interpolative proximal contractive condition that ensures the existence of the best proximity points of fuzzy mappings in the complete non-archimedean fuzzy metric spaces. We establish certain best proximity point theorems for such proximal contractions. We improve and generalize the fuzzy proximal contractions by introducing fuzzy proximal interpolative contractions. The obtained results improve and generalize the best proximity point theorems published in Fuzzy Information and Engineering, 5 (2013), 417–429. Moreover, we provide many nontrivial examples to validate our best proximity point theorem.

Keywords

best proximity pointgeneralized fuzzy interpolative proximal contractionsfuzzy metric space
CLC number: 47H10, 26E05, 26E25

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AIMS Mathematics
Volume 8 Issue 2,
February 2023
Pages 2891-2909
DOI: 10.3934/math.2023151

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Cite this article:
Javed K, Nazam M, Jahangeer F, et al. A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces. AIMS Mathematics, 2023, 8(2): 2891-2909. https://doi.org/10.3934/math.2023151

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Received: 07 July 2022
Revised: 30 October 2022
Accepted: 02 November 2022
Published: 15 February 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)