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Research Article | Open Access

Relation-theoretic almost ϕ-contractions with an application to elastic beam equations

Ebrahem A. Algehyne( ), Nifeen Hussain Altaweel, Mounirah Areshi, Faizan Ahmad Khan( )
Department of Mathematics, University of Tabuk, Tabuk-71491, Saudi Arabia
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Abstract

In this article, we prove some results on existence and uniqueness of fixed points for an almost ϕ-contraction mapping defined on a metric space endowed with an amorphous relation. Our results generalize and improve several well known fixed point theorems of the existing literature. To substantiate the credibility of our results, we construct some examples. We also apply our results to determine a unique solution of a boundary value problem associated with nonlinear elastic beam equations.

Keywords

almost contractionsboundary value problemsfixed pointsbinary relations
CLC number: 06A75, 34B15, 46T99, 47H10, 54H25

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18919-18929
DOI: 10.3934/math.2023963

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Cite this article:
Algehyne EA, Altaweel NH, Areshi M, et al. Relation-theoretic almost ϕ-contractions with an application to elastic beam equations. AIMS Mathematics, 2023, 8(8): 18919-18929. https://doi.org/10.3934/math.2023963

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Received: 03 April 2023
Revised: 15 May 2023
Accepted: 16 May 2023
Published: 15 August 2023
©2023 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)