Common fixed point results in $ \mathcal{F} $-metric spaces with application to nonlinear neutral differential equation

Hanadi Zahed; Ahmed Al-Rawashdeh; Jamshaid Ahmad; Hanadi Zahed; Ahmed Al-Rawashdeh; Jamshaid Ahmad

doi:10.3934/math.2023237

AIMS Mathematics

2023, Volume 8, Issue 2: 4786-4805. doi: 10.3934/math.2023237

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Research article

Common fixed point results in $ \mathcal{F} $-metric spaces with application to nonlinear neutral differential equation

1.
Department of Mathematics, College of Science, Taibah University, Madina, 41411, Saudi Arabia
2.
Department of Mathematical Sciences, UAE University, Al Ain, 15551, UAE
3.
Department of Mathematics, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 12 October 2022 Revised: 21 November 2022 Accepted: 22 November 2022 Published: 08 December 2022
MSC : 46S40, 47H10, 54H25

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of $ \mathcal{F} $-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of $ \mathcal{F} $-metric space equipped with a directed graph $ G $ are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation.
- fixed point,
- $ \mathcal{F} $-metric space,
- generalized contractions,
- control functions,
- differential equation
Citation: Hanadi Zahed, Ahmed Al-Rawashdeh, Jamshaid Ahmad. Common fixed point results in $ \mathcal{F} $-metric spaces with application to nonlinear neutral differential equation[J]. AIMS Mathematics, 2023, 8(2): 4786-4805. doi: 10.3934/math.2023237

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Abstract

The aim of this article is to obtain common fixed point results for generalized contractions involving control functions of two variables in the context of $ \mathcal{F} $-metric spaces. We also furnish an example to show the originality of our main result. Some results in the context of $ \mathcal{F} $-metric space equipped with a directed graph $ G $ are also established. As an application, we discuss the existence of solution to nonlinear neutral differential equation.

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