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Volume 14
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10.3390/axioms14120891
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Article

Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions

by
Nicola Fabiano
1,
Zouaoui Bekri
2,3,
Amir Baklouti
4,* and
Saber Mansour
5
1
“Vinča” Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12-14, 11351 Belgrade, Serbia
2
Laboratory of Fundamental and Applied Mathematics, University of Oran 1, Ahmed Ben Bella, Es-Senia 31000, Algeria
3
Department of Sciences and Technology, Institute of Sciences, Nour-Bachir University Center, El-Bayadh 32000, Algeria
4
Department of Mathematics, College of Science, Sfax University, Sfax 3029, Tunisia
5
Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, P.O. Box 14035, Holy Makkah 21955, Saudi Arabia
*
Author to whom correspondence should be addressed.
Axioms 2025, 14(12), 891; https://doi.org/10.3390/axioms14120891 (registering DOI)
Submission received: 6 November 2025 / Revised: 24 November 2025 / Accepted: 26 November 2025 / Published: 30 November 2025
(This article belongs to the Section Algebra and Number Theory)
Versions Notes

Abstract

We establish the existence and uniqueness of solutions to a class of second-order nonlinear boundary value problems involving impulses, delay, and possible singularities. The approach leverages the recent notion of paired-Chatterjea-type contractions. Under a smallness condition ensuring the associated integral operator is a Banach contraction with constant μ<13, we show that it is also a Chatterjea, and hence, a paired-Chatterjea contraction. By the fixed point theorem of Chand, this guarantees at most two fixed points; a supplementary uniqueness argument then ensures a unique solution in the Banach space PC1([a,b]).
Keywords: Banach contraction; paired-Chatterjea-type contractions; Chatterjea contraction; Lipschitz condition; fixed point theorem; existence and uniqueness Banach contraction; paired-Chatterjea-type contractions; Chatterjea contraction; Lipschitz condition; fixed point theorem; existence and uniqueness

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MDPI and ACS Style

Fabiano, N.; Bekri, Z.; Baklouti, A.; Mansour, S. Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions. Axioms 2025, 14, 891. https://doi.org/10.3390/axioms14120891

AMA Style

Fabiano N, Bekri Z, Baklouti A, Mansour S. Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions. Axioms. 2025; 14(12):891. https://doi.org/10.3390/axioms14120891

Chicago/Turabian Style

Fabiano, Nicola, Zouaoui Bekri, Amir Baklouti, and Saber Mansour. 2025. "Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions" Axioms 14, no. 12: 891. https://doi.org/10.3390/axioms14120891

APA Style

Fabiano, N., Bekri, Z., Baklouti, A., & Mansour, S. (2025). Existence and Uniqueness of Solutions to Singular Impulsive Delay Boundary Value Problems via Paired-Chatterjea-Type Contractions. Axioms, 14(12), 891. https://doi.org/10.3390/axioms14120891

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