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Research Article | Open Access

Interpolative best proximity point results via γ -contraction with applications

Department of Mathematics, Gazi University, Teknikokullar, Ankara, 06560, Turkey
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Abstract

In this paper, we introduce a ρ-interpolative Kannan and Ćirić-Reich-Rus type fuzzy proximal contraction using a γ-contraction. We prove some best proximity theorems of this new approximation using the concept of ρ-proximal admissibility in complete fuzzy metric spaces. We generalize some previous studies and present fixed point results of the best proximity theorems in complete fuzzy metric spaces. Also, we extend some best proximity results to the partially ordered fuzzy metric spaces.

Keywords

fuzzy metric spaceordered fuzzy metric spaceinterpolative proximal fuzzy contraction
CLC number: 47H10, 54H25

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AIMS Mathematics
Volume 10 Issue 1,
January 2025
Pages 1350-1366
DOI: 10.3934/math.2025062

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Cite this article:
Sezen MS. Interpolative best proximity point results via γ -contraction with applications. AIMS Mathematics, 2025, 10(1): 1350-1366. https://doi.org/10.3934/math.2025062

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Received: 21 October 2024
Revised: 06 January 2025
Accepted: 13 January 2025
Published: 15 January 2025
©2025 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)