Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

Hasanen A. Hammad; Hassen Aydi; Choonkil Park; Hasanen A. Hammad; Hassen Aydi; Choonkil Park

doi:10.3934/math.2022501

AIMS Mathematics

2022, Volume 7, Issue 5: 9003-9022. doi: 10.3934/math.2022501

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Research article

Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

1.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
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.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea

Received: 06 December 2021 Revised: 30 January 2022 Accepted: 21 February 2022 Published: 08 March 2022
MSC : 34B15, 47H10, 54H25

The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F$ _{\text{CM}} $-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy method to discuss the existence of fixed points. Also, the existence and uniqueness solution for a system of Volterra integral equations are studied by the theoretical results.
- tripled fixed point,
- fuzzy cone metric spaces,
- Lebesgue-integrable mapping,
- Volterra integral equation
Citation: Hasanen A. Hammad, Hassen Aydi, Choonkil Park. Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces[J]. AIMS Mathematics, 2022, 7(5): 9003-9022. doi: 10.3934/math.2022501

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Abstract

The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F$ _{\text{CM}} $-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy method to discuss the existence of fixed points. Also, the existence and uniqueness solution for a system of Volterra integral equations are studied by the theoretical results.

References

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