Convergence Criteria of Three Step Schemes for Solving Equations
We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative n...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/23/3106 |
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| author | Samundra Regmi Christopher I. Argyros Ioannis K. Argyros Santhosh George |
| author_facet | Samundra Regmi Christopher I. Argyros Ioannis K. Argyros Santhosh George |
| author_sort | Samundra Regmi |
| collection | DOAJ |
| description | We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence. |
| first_indexed | 2024-03-10T04:48:07Z |
| format | Article |
| id | doaj.art-2b1b8ec22d11485bb4aa07fcaf4b535e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T04:48:07Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2b1b8ec22d11485bb4aa07fcaf4b535e2023-11-23T02:46:08ZengMDPI AGMathematics2227-73902021-12-01923310610.3390/math9233106Convergence Criteria of Three Step Schemes for Solving EquationsSamundra Regmi0Christopher I. Argyros1Ioannis K. Argyros2Santhosh George3Learning Commons, University of North Texas at Dallas, Dallas, TX 75201, USADepartment of Computing and Technology, Cameron University, Lawton, OK 73505, USADepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore 575 025, IndiaWe develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expansions and the existence of the sixth derivative not on these schemes. So, the usage of them is restricted six or higher differentiable mappings. But in our paper only the first Frèchet derivative is utilized to show convergence. Consequently, the scheme is expanded. Numerical applications are also given to test convergence.https://www.mdpi.com/2227-7390/9/23/3106iterative schemesconvergence criterionBanach space |
| spellingShingle | Samundra Regmi Christopher I. Argyros Ioannis K. Argyros Santhosh George Convergence Criteria of Three Step Schemes for Solving Equations Mathematics iterative schemes convergence criterion Banach space |
| title | Convergence Criteria of Three Step Schemes for Solving Equations |
| title_full | Convergence Criteria of Three Step Schemes for Solving Equations |
| title_fullStr | Convergence Criteria of Three Step Schemes for Solving Equations |
| title_full_unstemmed | Convergence Criteria of Three Step Schemes for Solving Equations |
| title_short | Convergence Criteria of Three Step Schemes for Solving Equations |
| title_sort | convergence criteria of three step schemes for solving equations |
| topic | iterative schemes convergence criterion Banach space |
| url | https://www.mdpi.com/2227-7390/9/23/3106 |
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