Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications
A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1942 |
| _version_ | 1797522994625511424 |
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| author | Ioannis K. Argyros |
| author_facet | Ioannis K. Argyros |
| author_sort | Ioannis K. Argyros |
| collection | DOAJ |
| description | A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper. |
| first_indexed | 2024-03-10T08:37:12Z |
| format | Article |
| id | doaj.art-86829a7770bd4fd0ab3f4b8d32a68cb5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:12Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-86829a7770bd4fd0ab3f4b8d32a68cb52023-11-22T08:34:13ZengMDPI AGMathematics2227-73902021-08-01916194210.3390/math9161942Unified Convergence Criteria for Iterative Banach Space Valued Methods with ApplicationsIoannis K. Argyros0Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USAA plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible to provide unified convergence criteria for single-step iterative methods, which are weaker than earlier ones without additional hypotheses? The answer is yes. In particular, we provide only one sufficient convergence criterion suitable for single-step methods. Moreover, we also give a finer convergence analysis. Numerical experiments involving boundary value problems and Hammerstein-like integral equations complete this paper.https://www.mdpi.com/2227-7390/9/16/1942single step methodsBanach spaceconvergence criterion |
| spellingShingle | Ioannis K. Argyros Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications Mathematics single step methods Banach space convergence criterion |
| title | Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications |
| title_full | Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications |
| title_fullStr | Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications |
| title_full_unstemmed | Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications |
| title_short | Unified Convergence Criteria for Iterative Banach Space Valued Methods with Applications |
| title_sort | unified convergence criteria for iterative banach space valued methods with applications |
| topic | single step methods Banach space convergence criterion |
| url | https://www.mdpi.com/2227-7390/9/16/1942 |
| work_keys_str_mv | AT ioanniskargyros unifiedconvergencecriteriaforiterativebanachspacevaluedmethodswithapplications |