Interpolative best proximity point results via $ \mathbf{\gamma } $-contraction with applications

Müzeyyen Sangurlu Sezen; Müzeyyen Sangurlu Sezen

doi:10.3934/math.2025062

AIMS Mathematics

2025, Volume 10, Issue 1: 1350-1366. doi: 10.3934/math.2025062

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Research article

Interpolative best proximity point results via $ \mathbf{\gamma } $-contraction with applications

Müzeyyen Sangurlu Sezen ^,

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

Received: 21 October 2024 Revised: 06 January 2025 Accepted: 13 January 2025 Published: 21 January 2025
MSC : 47H10, 54H25

In this paper, we introduce a $ \rho $-interpolative Kannan and Ćirić-Reich-Rus type fuzzy proximal contraction using a $ \gamma $-contraction. We prove some best proximity theorems of this new approximation using the concept of $ \rho $-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.
- fuzzy metric space,
- ordered fuzzy metric space,
- interpolative proximal fuzzy contraction
Citation: Müzeyyen Sangurlu Sezen. Interpolative best proximity point results via $ \mathbf{\gamma } $-contraction with applications[J]. AIMS Mathematics, 2025, 10(1): 1350-1366. doi: 10.3934/math.2025062

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Abstract

In this paper, we introduce a $ \rho $-interpolative Kannan and Ćirić-Reich-Rus type fuzzy proximal contraction using a $ \gamma $-contraction. We prove some best proximity theorems of this new approximation using the concept of $ \rho $-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.

References

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