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

Khalil Javed; Muhammad Nazam; Fahad Jahangeer; Muhammad Arshad; Manuel De La Sen; Khalil Javed; Muhammad Nazam; Fahad Jahangeer; Muhammad Arshad; Manuel De La Sen

doi:10.3934/math.2023151

AIMS Mathematics

2023, Volume 8, Issue 2: 2891-2909. doi: 10.3934/math.2023151

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

1.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan
2.
Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad, Pakistan
3.
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

Received: 07 July 2022 Revised: 30 October 2022 Accepted: 02 November 2022 Published: 11 November 2022
MSC : 47H10, 26E05, 26E25

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.
- best proximity point,
- generalized fuzzy interpolative proximal contractions,
- fuzzy metric space
Citation: Khalil Javed, Muhammad Nazam, Fahad Jahangeer, Muhammad Arshad, Manuel De La Sen. A new approach to generalized interpolative proximal contractions in non archimedean fuzzy metric spaces[J]. AIMS Mathematics, 2023, 8(2): 2891-2909. doi: 10.3934/math.2023151

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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.

References

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