Some new characterizations and results for fuzzy contractions in fuzzy $ b $-metric spaces and applications

Haitham Qawaqneh; Mohd Salmi Md Noorani; Hassen Aydi; Haitham Qawaqneh; Mohd Salmi Md Noorani; Hassen Aydi

doi:10.3934/math.2023338

AIMS Mathematics

2023, Volume 8, Issue 3: 6682-6696. doi: 10.3934/math.2023338

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Research article

Some new characterizations and results for fuzzy contractions in fuzzy $ b $-metric spaces and applications

1.
Department of Mathematics, Faculty of Science and Information Technology, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
2.
School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, Malaysia
3.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
4.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 25 August 2022 Revised: 13 December 2022 Accepted: 20 December 2022 Published: 06 January 2023
MSC : 47H10, 54H25, 46J10

In this work, we initiate the notion of a fuzzy cyclic $ (\alpha, \beta) $-admissibility to establish some fixed point results for contraction mappings involving a generalized simulation function in the class of fuzzy $ b $-metric spaces. We give some illustrative examples to validate the new concepts and obtained results. At the end, we present an application on a Fredholm integral equation.
- fuzzy $ b $-metric space,
- simulation function,
- fixed point,
- integral equation
Citation: Haitham Qawaqneh, Mohd Salmi Md Noorani, Hassen Aydi. Some new characterizations and results for fuzzy contractions in fuzzy $ b $-metric spaces and applications[J]. AIMS Mathematics, 2023, 8(3): 6682-6696. doi: 10.3934/math.2023338

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Abstract

In this work, we initiate the notion of a fuzzy cyclic $ (\alpha, \beta) $-admissibility to establish some fixed point results for contraction mappings involving a generalized simulation function in the class of fuzzy $ b $-metric spaces. We give some illustrative examples to validate the new concepts and obtained results. At the end, we present an application on a Fredholm integral equation.

References

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