Nonlinear contractions on directed graphs with applications to boundary value problems

Doaa Filali; Mohammad Akram; Mohammad Dilshad; Doaa Filali; Mohammad Akram; Mohammad Dilshad

doi:10.3934/math.2024741

AIMS Mathematics

2024, Volume 9, Issue 6: 15263-15275. doi: 10.3934/math.2024741

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Research article

Nonlinear contractions on directed graphs with applications to boundary value problems

1.
Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh-11671, Saudi Arabia
2.
Department of Mathematics, Islamic University of Madinah, Madinah-42351, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia

Received: 17 February 2024 Revised: 07 April 2024 Accepted: 10 April 2024 Published: 28 April 2024
MSC : 34B15, 47H10, 54H25

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.
- $ {\rm(C)} $-graph,
- Cauchy equivalence,
- lower solution
Citation: Doaa Filali, Mohammad Akram, Mohammad Dilshad. Nonlinear contractions on directed graphs with applications to boundary value problems[J]. AIMS Mathematics, 2024, 9(6): 15263-15275. doi: 10.3934/math.2024741

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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.

References

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