Nonlinear contractions on directed graphs with applications to boundary value problems

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)

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