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Research Article | Open Access

Nonlinear almost F-contractions in relational metric space with an application to periodic boundary value problems

Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk-71491, Saudi Arabia
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Abstract

In this paper, we establish some fixed-point outcomes for a nonlinear almost F-contraction map in a metric space combined with a locally L -transitive binary relation. Numerous previous insights are expanded, developed, improved, and consolidated in the outcomes reported herein. We propose a few instances in order to illustrate our findings. As an application of our findings, we explore the existence of a solution of a first-order periodic boundary value problem.

Keywords

fixed pointsF-contractionsΓ-continuitylocally transitive relationsboundary value problems
CLC number: 34B15, 47H10, 54H25

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AIMS Mathematics
Volume 11 Issue 3,
March 2026
Pages 7593-7609
DOI: 10.3934/math.2026312

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Cite this article:
Alamer A, Khan FA. Nonlinear almost F-contractions in relational metric space with an application to periodic boundary value problems. AIMS Mathematics, 2026, 11(3): 7593-7609. https://doi.org/10.3934/math.2026312

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Received: 22 January 2026
Revised: 17 February 2026
Accepted: 27 February 2026
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)