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

Yahaya Jibrin Danjuma; Muhammed Raji; Isaac Adaji; Aminu Ibrahim

doi:10.5281/zenodo.21454260

Yahaya Jibrin Danjuma Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Muhammed Raji Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Isaac Adaji Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria
Aminu Ibrahim Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria

DOI: https://doi.org/10.5281/zenodo.21454260

Keywords: Fixed point, F-contraction, Extended F-weak contraction, α-F-weak contraction, Periodic points

Abstract

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

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