Common fixed points for ($ \kappa _{G_{m}} $)-contractions with applications

Jamshaid Ahmad; Abdullah Shoaib; Irshad Ayoob; Nabil Mlaiki; Jamshaid Ahmad; Abdullah Shoaib; Irshad Ayoob; Nabil Mlaiki

doi:10.3934/math.2024772

AIMS Mathematics

2024, Volume 9, Issue 6: 15949-15965. doi: 10.3934/math.2024772

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Research article

Common fixed points for ($ \kappa _{G_{m}} $)-contractions with applications

1.
Department of Mathematics and Statistics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia
2.
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
3.
Department of Mathematics and Sciences Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 06 January 2024 Revised: 04 April 2024 Accepted: 26 April 2024 Published: 06 May 2024
MSC : 46S40, 47H10, 54H25

In this publication, our objective was to introduce and establish the concepts of $ \kappa _{G_{m}} $-contraction and generalized $ (\alpha, \kappa _{G_{m}}) $-contraction in complete $ G_{m} $-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis.
- $ G_{m} $-metric space,
- fixed point,
- $ (\kappa _{G_{m}}) $ -contraction,
- generalized $ (\alpha, \kappa _{G_{m}}) $-contraction,
- integral equation
Citation: Jamshaid Ahmad, Abdullah Shoaib, Irshad Ayoob, Nabil Mlaiki. Common fixed points for ($ \kappa _{G_{m}} $)-contractions with applications[J]. AIMS Mathematics, 2024, 9(6): 15949-15965. doi: 10.3934/math.2024772

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Abstract

In this publication, our objective was to introduce and establish the concepts of $ \kappa _{G_{m}} $-contraction and generalized $ (\alpha, \kappa _{G_{m}}) $-contraction in complete $ G_{m} $-metric spaces, which led to the discovery of novel fixed points, coincidence points, and common fixed points. Additionally, we demonstrated the usefulness of our main results by applying it to the investigation of the integral equation. Also, we presenting a noteworthy example demonstrating the practicality of our primary hypothesis.

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