Relation-theoretic almost $ \phi $-contractions with an application to elastic beam equations

Ebrahem A. Algehyne; Nifeen Hussain Altaweel; Mounirah Areshi; Faizan Ahmad Khan; Ebrahem A. Algehyne; Nifeen Hussain Altaweel; Mounirah Areshi; Faizan Ahmad Khan

doi:10.3934/math.2023963

AIMS Mathematics

2023, Volume 8, Issue 8: 18919-18929. doi: 10.3934/math.2023963

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Research article

Relation-theoretic almost $ \phi $-contractions with an application to elastic beam equations

Department of Mathematics, University of Tabuk, Tabuk-71491, Saudi Arabia

Received: 03 April 2023 Revised: 15 May 2023 Accepted: 16 May 2023 Published: 05 June 2023
MSC : 06A75, 34B15, 46T99, 47H10, 54H25

In this article, we prove some results on existence and uniqueness of fixed points for an almost $ \phi $-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.
- almost contractions,
- boundary value problems,
- fixed points,
- binary relations
Citation: Ebrahem A. Algehyne, Nifeen Hussain Altaweel, Mounirah Areshi, Faizan Ahmad Khan. Relation-theoretic almost $ \phi $-contractions with an application to elastic beam equations[J]. AIMS Mathematics, 2023, 8(8): 18919-18929. doi: 10.3934/math.2023963

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Abstract

In this article, we prove some results on existence and uniqueness of fixed points for an almost $ \phi $-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.

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