Solution of integral equations for multivalued maps in fuzzy $ b $-metric spaces using Geraghty type contractions

Rashid Ali; Faisar Mehmood; Aqib Saghir; Hassen Aydi; Saber Mansour; Wajdi Kallel; Rashid Ali; Faisar Mehmood; Aqib Saghir; Hassen Aydi; Saber Mansour; Wajdi Kallel

doi:10.3934/math.2023851

AIMS Mathematics

2023, Volume 8, Issue 7: 16633-16654. doi: 10.3934/math.2023851

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Research article

Solution of integral equations for multivalued maps in fuzzy $ b $-metric spaces using Geraghty type contractions

1.
Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan, Email: rashid.ali@cust.edu.pk
2.
Institut Supérieur d'Informatique et des Techniques de Communication, Université de Sousse, H. Sousse 4000, Tunisia
3.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa
5.
Department of Mathematics, Umm Al-Qura University, Faculty of Applied sciences, P.O. Box 14035, Holly Makkah 21955, Saudi Arabia, Email: samansour@uqu.edu.sa, wfkallel@uqu.edu.sa

Received: 09 March 2023 Revised: 24 April 2023 Accepted: 27 April 2023 Published: 11 May 2023
MSC : 47H10, 54H25

In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.
- Geraghty type contractions,
- Hausdorff fuzzy $ b $-metric space,
- fuzzy $ b $-metric space,
- fuzzy metric space
Citation: Rashid Ali, Faisar Mehmood, Aqib Saghir, Hassen Aydi, Saber Mansour, Wajdi Kallel. Solution of integral equations for multivalued maps in fuzzy $ b $-metric spaces using Geraghty type contractions[J]. AIMS Mathematics, 2023, 8(7): 16633-16654. doi: 10.3934/math.2023851

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Abstract

In this article, the notion of Hausdorff fuzzy $ b $-metric space is studied. Some fixed point results for multivalued mappings using Geraghty type contractions in $ G $-complete fuzzy $ b $-metric spaces are established. To strengthen the results, an illustrative example is furnished. A fuzzy integral inclusion is constructed as an application of fixed point result which shows the validity of the proved results. The presented outcomes are the generalization of the existing results in literature.

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