On solution of Fredholm integral equations via fuzzy $ b $-metric spaces using triangular property

Gunaseelan Mani; Arul Joseph Gnanaprakasam; Absar Ul Haq; Imran Abbas Baloch; Choonkil Park; Gunaseelan Mani; Arul Joseph Gnanaprakasam; Absar Ul Haq; Imran Abbas Baloch; Choonkil Park

doi:10.3934/math.2022620

AIMS Mathematics

2022, Volume 7, Issue 6: 11102-11118. doi: 10.3934/math.2022620

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Research article

On solution of Fredholm integral equations via fuzzy $ b $-metric spaces using triangular property

1.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamil Nadu, India
2.
Department of Mathematics, College of Engineering and Technology, Faculty of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur 603203, Kanchipuram, Chennai, Tamil Nadu, India
3.
Department of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan
4.
Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan
5.
Higher Education Department, Govt. Graduate College for Boys Gulberg Lahore, Punjab, Pakistan
6.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 07 February 2022 Revised: 07 February 2022 Accepted: 31 March 2022 Published: 08 April 2022
MSC : 54H25, 47H10

In the present paper, we prove common fixed point without continuity by using triangular property on fuzzy $ b $-metric space. Our results generalize and expand some of the literature's well-known results. We also explore some of the application of our key results to Fredholm integral equation.
- fuzzy metric spaces,
- fuzzy $ b $-metric space,
- common fixed point
Citation: Gunaseelan Mani, Arul Joseph Gnanaprakasam, Absar Ul Haq, Imran Abbas Baloch, Choonkil Park. On solution of Fredholm integral equations via fuzzy $ b $-metric spaces using triangular property[J]. AIMS Mathematics, 2022, 7(6): 11102-11118. doi: 10.3934/math.2022620

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Abstract

In the present paper, we prove common fixed point without continuity by using triangular property on fuzzy $ b $-metric space. Our results generalize and expand some of the literature's well-known results. We also explore some of the application of our key results to Fredholm integral equation.

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