Extended rectangular fuzzy $ b $-metric space with application

Naeem Saleem; Salman Furqan; Mujahid Abbas; Fahd Jarad; Naeem Saleem; Salman Furqan; Mujahid Abbas; Fahd Jarad

doi:10.3934/math.2022885

AIMS Mathematics

2022, Volume 7, Issue 9: 16208-16230. doi: 10.3934/math.2022885

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Extended rectangular fuzzy $ b $-metric space with application

1.
Department of Mathematics, University of Management and Technology, Lahore 54000, Pakistan
2.
Department of Mathematics, Government College University, Lahore 54000, Pakistan
3.
Department of Medical Research, China Medical University, Taichung, Taiwan
4.
Department of Mathematics, Cankaya University, 06790 Etimesgut, Ankara, Turkey
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Received: 20 April 2022 Revised: 16 June 2022 Accepted: 23 June 2022 Published: 04 July 2022
MSC : 47H10, 54H25

In this paper, we introduce an extended rectangular fuzzy $ b $-metric space which generalizes rectangular fuzzy $ b $-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy $ b $-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ćirić type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy $ b $-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.
- fuzzy metric space,
- rectangular fuzzy $ b $-metric space,
- Ćirić type contractions,
- fixed points,
- integral equations
Citation: Naeem Saleem, Salman Furqan, Mujahid Abbas, Fahd Jarad. Extended rectangular fuzzy $ b $-metric space with application[J]. AIMS Mathematics, 2022, 7(9): 16208-16230. doi: 10.3934/math.2022885

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Abstract

In this paper, we introduce an extended rectangular fuzzy $ b $-metric space which generalizes rectangular fuzzy $ b $-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy $ b $-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ćirić type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy $ b $-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.

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