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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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Mathematics |
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| 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. |
| format | Article |
| id | doaj-art-cc29f8317895488d8108b254b63c9bae |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| 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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