Common fixed points of locally contractive mappings in bicomplex valued metric spaces with application to Urysohn integral equation

Nabil Mlaiki; Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei; Dania Santina; Nabil Mlaiki; Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei; Dania Santina

doi:10.3934/math.2023194

AIMS Mathematics

2023, Volume 8, Issue 2: 3897-3912. doi: 10.3934/math.2023194

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Common fixed points of locally contractive mappings in bicomplex valued metric spaces with application to Urysohn integral equation

1.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
4.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 21 September 2022 Revised: 17 November 2022 Accepted: 23 November 2022 Published: 29 November 2022
MSC : 46S40, 54H25, 47H10

The aim of this article is to obtain common fixed points of locally contractive mappings in the setting of bicomplex valued metric spaces. Our investigations generalize some conventional theorems of literature. Furthermore, we supply a significant example to manifest the authenticity of the proved results. As an application, we solve the solution of the integral equation by using our main result.
- common fixed point,
- bicomplex valued metric space,
- closed ball,
- generalized contractions,
- Urysohn integral equation
Citation: Nabil Mlaiki, Jamshaid Ahmad, Abdullah Eqal Al-Mazrooei, Dania Santina. Common fixed points of locally contractive mappings in bicomplex valued metric spaces with application to Urysohn integral equation[J]. AIMS Mathematics, 2023, 8(2): 3897-3912. doi: 10.3934/math.2023194

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Abstract

The aim of this article is to obtain common fixed points of locally contractive mappings in the setting of bicomplex valued metric spaces. Our investigations generalize some conventional theorems of literature. Furthermore, we supply a significant example to manifest the authenticity of the proved results. As an application, we solve the solution of the integral equation by using our main result.

References

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