Advancements in fixed point results for ordered metric space via extended F-weak contraction with applications

Abstract In (Ann. Math. Comp. Sc., 20, 82–97, 2024), Raji and Ibrahim introduced a new class of contractions, termed modified α-F-weak contractions, and established fixed point results in complete metric spaces, thereby extending the classical Banach contraction principle. Building on this, the present paper introduces an extended F-weak contraction mapping in ordered metric spaces and derives corresponding fixed-point results. The theoretical contributions are further illustrated through numerical examples. As an application, we demonstrate the existence and uniqueness of solutions to a first-order ordinary differential equation subject to periodic boundary conditions. Mathematics subject Classification 47H10; 54H25 Keywords: Fixed point, F-contraction, Extended F-weak contraction, α-F-weak contraction, Periodic points