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Research Article | Open Access

Nonlinear contractions on directed graphs with applications to boundary value problems

Doaa Filali1, Mohammad Akram2, Mohammad Dilshad3( )
Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh-11671, Saudi Arabia
Department of Mathematics, Islamic University of Madinah, Madinah-42351, Saudi Arabia
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia
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Abstract

This article contains some outcomes on fixed points for a graph preserving nonlinear contraction in a metric space endued with a transitive directed graph. Our results improved, enriched, and subsumed various known fixed point theorems. To argue for reliability of our results, we presented two examples. We concluded the manuscript to investigate a unique solution of a certain first-order boundary value problem by means of our results.

Keywords

(C)-graphCauchy equivalencelower solution
CLC number: 34B15, 47H10, 54H25

References

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AIMS Mathematics
Volume 9 Issue 6,
May 2024
Pages 15263-15275
DOI: 10.3934/math.2024741

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Cite this article:
Filali D, Akram M, Dilshad M. Nonlinear contractions on directed graphs with applications to boundary value problems. AIMS Mathematics, 2024, 9(6): 15263-15275. https://doi.org/10.3934/math.2024741

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Received: 17 February 2024
Revised: 07 April 2024
Accepted: 10 April 2024
Published: 28 April 2024
©2024 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)