Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction

A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular...

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Main Authors: Kanyuta Poochinapan, Sompop Moonchai, Tanadon Chaobankoh, Phakdi Charoensawan
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/13/10/1569
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author Kanyuta Poochinapan
Sompop Moonchai
Tanadon Chaobankoh
Phakdi Charoensawan
author_facet Kanyuta Poochinapan
Sompop Moonchai
Tanadon Chaobankoh
Phakdi Charoensawan
author_sort Kanyuta Poochinapan
collection DOAJ
description A new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems.
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issn 2227-7390
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spelling doaj-art-cc29f8317895488d8108b254b63c9bae2025-08-20T03:14:35ZengMDPI AGMathematics2227-73902025-05-011310156910.3390/math13101569Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based ContractionKanyuta Poochinapan0Sompop Moonchai1Tanadon Chaobankoh2Phakdi Charoensawan3Advanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, ThailandAdvanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, ThailandAdvanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, ThailandAdvanced Research Center for Computational Simulation, Chiang Mai University, Chiang Mai 50200, ThailandA new kind of graph-based contraction in a metric space is introduced in this article. We investigate results concerning the best proximity points and fixed points for these contractions, supported by illustrated examples. The practical applicability of our results is demonstrated through particular instances in the setting of integral equations and differential equations. We also describe how a class of third-order boundary value problems satisfying the present contraction can be solved iteratively. To support our findings, we conduct a series of numerical experiments with various third-order boundary value problems.https://www.mdpi.com/2227-7390/13/10/1569contractiondifferential equationintegral equation
spellingShingle Kanyuta Poochinapan
Sompop Moonchai
Tanadon Chaobankoh
Phakdi Charoensawan
Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
Mathematics
contraction
differential equation
integral equation
title Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
title_full Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
title_fullStr Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
title_full_unstemmed Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
title_short Existence of Solution to Nonlinear Third-Order Differential Equation and Iterative Method Utilization via Graph-Based Contraction
title_sort existence of solution to nonlinear third order differential equation and iterative method utilization via graph based contraction
topic contraction
differential equation
integral equation
url https://www.mdpi.com/2227-7390/13/10/1569
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AT sompopmoonchai existenceofsolutiontononlinearthirdorderdifferentialequationanditerativemethodutilizationviagraphbasedcontraction
AT tanadonchaobankoh existenceofsolutiontononlinearthirdorderdifferentialequationanditerativemethodutilizationviagraphbasedcontraction
AT phakdicharoensawan existenceofsolutiontononlinearthirdorderdifferentialequationanditerativemethodutilizationviagraphbasedcontraction