A Fixed-Point Chatterjea–Singh Mapping Approach: Existence and Uniqueness of Solutions to Nonlinear BVPs

Zouaoui Bekri (), Nicola Fabiano, Abdulaziz Khalid Alsharidi () and Mohammed Ahmed Alomair
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Zouaoui Bekri: Laboratory of Fundamental and Applied Mathematics, University of Oran 1, Ahmed Ben Bella, Es-Senia 31000, Algeria
Nicola Fabiano: “Vinča” Institute of Nuclear Sciences—National Institute of the Republic of Serbia, University of Belgrade, 11351 Belgrade, Serbia
Abdulaziz Khalid Alsharidi: Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia
Mohammed Ahmed Alomair: Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Mathematics, 2025, vol. 13, issue 20, 1-8

Abstract: This paper introduces an application of the Chatterjea–Singh fixed-point theorem to nonlinear boundary value problems (BVPs). We define a Chatterjea–Singh mapping as one whose iterate T p satisfies a Chatterjea-type contractive condition. Under this weaker assumption than classical Banach or Chatterjea contractions, we prove the existence and uniqueness of solutions to second-order BVPs. Our method applies even when T itself does not satisfy a contraction property. Examples illustrate how iteration can recover convergence where standard conditions fail. This work extends generalized fixed-point theory in differential equations and highlights the flexibility of delayed contraction criteria.

Keywords: Chatterjea contraction; Singh mapping; fixed-point theorem; boundary value problem; Green’s function; iterative contraction; existence and uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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