Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations
In this paper, we introduce a new class of mappings called “generalized <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantic...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/3/723 |
| _version_ | 1797608842548215808 |
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| author | Hasanen A. Hammad Kamaleldin Abodayeh Wasfi Shatanawi |
| author_facet | Hasanen A. Hammad Kamaleldin Abodayeh Wasfi Shatanawi |
| author_sort | Hasanen A. Hammad |
| collection | DOAJ |
| description | In this paper, we introduce a new class of mappings called “generalized <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding. |
| first_indexed | 2024-03-11T05:50:14Z |
| format | Article |
| id | doaj.art-6c20bdd23e754428a7d2d51414348f7f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T05:50:14Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6c20bdd23e754428a7d2d51414348f7f2023-11-17T14:10:07ZengMDPI AGSymmetry2073-89942023-03-0115372310.3390/sym15030723Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential EquationsHasanen A. Hammad0Kamaleldin Abodayeh1Wasfi Shatanawi2Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaIn this paper, we introduce a new class of mappings called “generalized <inline-formula><math display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-Geraghty contraction-type mappings”. We use our new class to formulate and prove some coupled fixed points in the setting of partially ordered metric spaces. Our results generalize and unite several findings known in the literature. We also provide some examples to support and illustrate our theoretical results. Furthermore, we apply our results to discuss the existence and uniqueness of a solution to a coupled ordinary differential equation as an application of our finding.https://www.mdpi.com/2073-8994/15/3/723extended <i>β</i>-<i>ϕ</i>-Geraghty contraction mappinggeneralized triangular <i>β</i>-admissible mappingcoupled fixed pointordinary differential equation |
| spellingShingle | Hasanen A. Hammad Kamaleldin Abodayeh Wasfi Shatanawi Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations Symmetry extended <i>β</i>-<i>ϕ</i>-Geraghty contraction mapping generalized triangular <i>β</i>-admissible mapping coupled fixed point ordinary differential equation |
| title | Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations |
| title_full | Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations |
| title_fullStr | Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations |
| title_full_unstemmed | Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations |
| title_short | Applying an Extended <em>β</em>-<em>ϕ</em>-Geraghty Contraction for Solving Coupled Ordinary Differential Equations |
| title_sort | applying an extended em β em em ϕ em geraghty contraction for solving coupled ordinary differential equations |
| topic | extended <i>β</i>-<i>ϕ</i>-Geraghty contraction mapping generalized triangular <i>β</i>-admissible mapping coupled fixed point ordinary differential equation |
| url | https://www.mdpi.com/2073-8994/15/3/723 |
| work_keys_str_mv | AT hasanenahammad applyinganextendedembememphemgeraghtycontractionforsolvingcoupledordinarydifferentialequations AT kamaleldinabodayeh applyinganextendedembememphemgeraghtycontractionforsolvingcoupledordinarydifferentialequations AT wasfishatanawi applyinganextendedembememphemgeraghtycontractionforsolvingcoupledordinarydifferentialequations |