Convergence and Stability Results for a New Inertial-Type IterativeScheme of Coupled Coincidence Points in G-Metric Spaces andApplications to Integral Systems and Differential Equations

Elvin Rada

doi:10.23918/eajse.v11i3p20

Authors

Elvin Rada Department of Mathematics, Faculty of Natural Sciences, University of Elbasan "Aleksandër Xhuvani", Albania https://orcid.org/0000-0003-3751-2889

DOI:

https://doi.org/10.23918/eajse.v11i3p20

Keywords:

Coupled coincidence point, G-metric space, inertial iteration, stability, nonlinear analysis, Volterra integral systems, Systems of differential equations

Abstract

In this paper, I develop an inertial-type iterative scheme, equipped with perturbation terms, for approximating coupled coincidence points of nonlinear operators using the G-metric space setting. The construction brings together several well-known fixed point procedures, such as the Picard, Mann, Ishikawa and Noor iterations, and extends them within a single unified framework. Under a suitable coupled G-contractive condition, I show that the sequence generated by my inertial-type iteration converges strongly to the unique coupled coincidence point. I also establish Ulam–Hyers and furthermore Ulam–Hyers–Rassias stability and obtain a linear rate of convergence. To demonstrate the usefulness of the approach, I apply the scheme to coupled nonlinear Volterra integral equations and to systems of differential equations.

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