On fixed point results in $ \mathcal{F} $-metric spaces with applications

Hanadi Zahed; Zhenhua Ma; Jamshaid Ahmad; Hanadi Zahed; Zhenhua Ma; Jamshaid Ahmad

doi:10.3934/math.2023863

AIMS Mathematics

2023, Volume 8, Issue 7: 16887-16905. doi: 10.3934/math.2023863

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Research article

On fixed point results in $ \mathcal{F} $-metric spaces with applications

Hanadi Zahed ^{1
,},
Zhenhua Ma ^{2
,
,},
Jamshaid Ahmad ^{3
,}

1.
Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara 41411, Saudi Arabia, Email: hzahed@taibahu.edu.sa
2.
Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China, Email: mazhenghua_1981@163.com
3.
Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia, Email: jkhan@uj.edu.sa

Received: 28 February 2023 Revised: 19 April 2023 Accepted: 27 April 2023 Published: 15 May 2023
MSC : 46S40, 54H25, 47H10

The aim of this research article is to define locally rational contractions concerning control functions of one variable in the background of $ \mathcal{F} $-metric spaces and establish common fixed point results. We also introduce ($ \alpha ^{\ast } $-$ \psi) $-contractions and generalized ($ \alpha ^{\ast } $, $ \psi, \delta _{\mathcal{F}}) $-contractions in $ \mathcal{F} $-metric spaces and obtain fixed points of multifunctions. A non trivial example is also furnished to manifest the originality of the fundamental result. As application, we investigate the solution of nonlinear neutral differential equation.
Citation: Hanadi Zahed, Zhenhua Ma, Jamshaid Ahmad. On fixed point results in $ \mathcal{F} $-metric spaces with applications[J]. AIMS Mathematics, 2023, 8(7): 16887-16905. doi: 10.3934/math.2023863

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Abstract

The aim of this research article is to define locally rational contractions concerning control functions of one variable in the background of $ \mathcal{F} $-metric spaces and establish common fixed point results. We also introduce ($ \alpha ^{\ast } $-$ \psi) $-contractions and generalized ($ \alpha ^{\ast } $, $ \psi, \delta _{\mathcal{F}}) $-contractions in $ \mathcal{F} $-metric spaces and obtain fixed points of multifunctions. A non trivial example is also furnished to manifest the originality of the fundamental result. As application, we investigate the solution of nonlinear neutral differential equation.

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