New Fixed Point Principles Based on Decreasing Auxiliary Functions and Their Applications

Rabeb Sidaoui, Hayel N. Saleh, Amel Touati and Khaled Aldwoah

Journal of Mathematics, 2026, vol. 2026, 1-12

Abstract: This work introduces a novel contractive framework, referred to as the G-contraction, which is formulated via a decreasing function G:0,∞⟶0,∞ satisfying a collection of axioms distinct from those associated with F-contractions and θ-contractions. Within this setting, some fixed point theorems are established and new consequences are derived. The approach used to prove our main results differs from existing methods, as it relies on the fact that G is a bijection. An illustrative example is also provided to show that the proposed class properly extends the classical Banach contraction principle. As an application, we investigate a nonlinear fractional boundary value problem subject to a nonlocal condition.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8468823

DOI: 10.1155/jom/8468823

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