Nonlinear contractions on directed graphs with applications to boundary value problems-Reference-Cited by-同舟云学术

Nonlinear contractions on directed graphs with applications to boundary value problems

Published:2024 Issue:6 Volume:9 Page:15263-15275
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Filali Doaa¹,Akram Mohammad²,Dilshad Mohammad³

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference18 articles.

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3. J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359–1373.

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5. F. Bojor, Fixed point of $\phi$-contraction in metric spaces endowed with a graph, Ann. Univ. Craiova Mat., 37 (2010), 85–92. https://doi.org/10.52846/ami.v37i4.374

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