Convergence analysis of hybrid interpolative contractions with applications to RLC circuits and nonlinear hinged biharmonic problems

Wardah; Mujahid Abbas; Haroon Ahmad; Mudasir Younis; Lateef Ahmad Wani; Wardah; Mujahid Abbas; Haroon Ahmad; Mudasir Younis; Lateef Ahmad Wani

doi:10.3934/math.2026989

AIMS Mathematics

2026, Volume 11, Issue 8: 24525-24551. doi: 10.3934/math.2026989

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Convergence analysis of hybrid interpolative contractions with applications to RLC circuits and nonlinear hinged biharmonic problems

1.
Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
2.
Department of Mechanical Engineering Sciences, Faculty of Engineering and the Built Environment, Doornfontein Campus, University of Johannesburg, South Africa
3.
Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya, 54050 Turkey
4.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
5.
Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

Received: 05 June 2026 Revised: 27 July 2026 Accepted: 29 July 2026 Published: 11 August 2026
MSC : 34B27, 45B05, 47H10, 54H25

This work investigates a limitation associated with interpolative contraction mappings, where the contractive conditions are generally not imposed at fixed points, resulting in conditions that are not valid over the entire domain. To overcome this drawback, we introduce novel hybrid interpolative contractions, specifically the hybrid interpolative-Kannan and the hybrid interpolative Reich–Rus–Čirić types. By suitably modifying the interpolative structure through an additional control term, the proposed contractive conditions hold on the entire domain, including fixed points. Using this hybrid framework, we establish rigorous existence and uniqueness results for fixed points of the associated self-mappings in metric spaces. The strength and enrichment of the theory are demonstrated through explicit continuous and discontinuous examples that satisfy the hybrid conditions but fail the classical interpolative ones. Finally, we illustrate the applicability of our results by studying an Resistor-Inductor-Capacitor (RLC) circuit system and a nonlinear biharmonic problem with hinged boundary conditions, where the existence and uniqueness of solutions are guaranteed via the proposed hybrid interpolative contractions.
- fixed point,
- hybrid interpolative contraction,
- biharmonic problem,
- RLC circuit system
Citation: Wardah, Mujahid Abbas, Haroon Ahmad, Mudasir Younis, Lateef Ahmad Wani. Convergence analysis of hybrid interpolative contractions with applications to RLC circuits and nonlinear hinged biharmonic problems[J]. AIMS Mathematics, 2026, 11(8): 24525-24551. doi: 10.3934/math.2026989

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Abstract

This work investigates a limitation associated with interpolative contraction mappings, where the contractive conditions are generally not imposed at fixed points, resulting in conditions that are not valid over the entire domain. To overcome this drawback, we introduce novel hybrid interpolative contractions, specifically the hybrid interpolative-Kannan and the hybrid interpolative Reich–Rus–Čirić types. By suitably modifying the interpolative structure through an additional control term, the proposed contractive conditions hold on the entire domain, including fixed points. Using this hybrid framework, we establish rigorous existence and uniqueness results for fixed points of the associated self-mappings in metric spaces. The strength and enrichment of the theory are demonstrated through explicit continuous and discontinuous examples that satisfy the hybrid conditions but fail the classical interpolative ones. Finally, we illustrate the applicability of our results by studying an Resistor-Inductor-Capacitor (RLC) circuit system and a nonlinear biharmonic problem with hinged boundary conditions, where the existence and uniqueness of solutions are guaranteed via the proposed hybrid interpolative contractions.

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