Multivalued contraction maps on fuzzy $ b $-metric spaces and an application

Samina Batul; Faisar Mehmood; Azhar Hussain; Dur-e-Shehwar Sagheer; Hassen Aydi; Aiman Mukheimer; Samina Batul; Faisar Mehmood; Azhar Hussain; Dur-e-Shehwar Sagheer; Hassen Aydi; Aiman Mukheimer

doi:10.3934/math.2022330

AIMS Mathematics

2022, Volume 7, Issue 4: 5925-5942. doi: 10.3934/math.2022330

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Research article

Multivalued contraction maps on fuzzy $ b $-metric spaces and an application

1.
Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan
2.
Department of Mathematics, University of Sargodha, Sargodha-40100, Pakistan
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
6.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 20 November 2021 Revised: 31 December 2021 Accepted: 04 January 2022 Published: 13 January 2022
MSC : 46S40, 47H10, 54H25

In this article, the concept of a Hausdorff fuzzy $ b $-metric space is introduced. The new notion is used to establish some fixed point results for multivalued mappings in $ G $-complete fuzzy $ b $-metric spaces satisfying a suitable requirement of contractiveness. An illustrative example is formulated to support the results. Eventually, an application for the existence of a solution for an integral inclusion is established which involves showing the materiality of the obtained results. These results are more general and some theorems proved by of Shehzad et al. are their special cases.
- fuzzy $ b $-metric space,
- Hausdorff fuzzy $ b $-metric space,
- fixed point,
- multivalued mapping
Citation: Samina Batul, Faisar Mehmood, Azhar Hussain, Dur-e-Shehwar Sagheer, Hassen Aydi, Aiman Mukheimer. Multivalued contraction maps on fuzzy $ b $-metric spaces and an application[J]. AIMS Mathematics, 2022, 7(4): 5925-5942. doi: 10.3934/math.2022330

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Abstract

In this article, the concept of a Hausdorff fuzzy $ b $-metric space is introduced. The new notion is used to establish some fixed point results for multivalued mappings in $ G $-complete fuzzy $ b $-metric spaces satisfying a suitable requirement of contractiveness. An illustrative example is formulated to support the results. Eventually, an application for the existence of a solution for an integral inclusion is established which involves showing the materiality of the obtained results. These results are more general and some theorems proved by of Shehzad et al. are their special cases.

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