SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION
The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces. In this article, the imposed hypotheses is amiable than the well-known Lipschitz and Hölder continuity conditions. The R-order converge...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2020-04-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | http://www.utgjiu.ro/math/sma/v15/p15_12.pdf |
| _version_ | 1818362400822263808 |
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| author | Neha Gupta Jai Prakash Jaiswal |
| author_facet | Neha Gupta Jai Prakash Jaiswal |
| author_sort | Neha Gupta |
| collection | DOAJ |
| description | The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces. In this article, the imposed hypotheses is amiable than the well-known Lipschitz and Hölder continuity conditions. The R-order convergence of the considered scheme is proved to be at least 4+3q. An approximate apriori error bound for this method is also elaborated and the domain of existence and uniqueness of the solution in the convergence theorem. Two numerical illustrations have been worked out to exhibit the virtue of the developed theory. |
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| format | Article |
| id | doaj.art-2b4d4a0ee2a64dcb8829238c8fb4ebc1 |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-12-13T21:31:59Z |
| publishDate | 2020-04-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-2b4d4a0ee2a64dcb8829238c8fb4ebc12022-12-21T23:30:46ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982020-04-0115 (2020)325339SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITIONNeha Gupta0Jai Prakash Jaiswal1Maulana Azad National Institute of Technology, Bhopal, M.P. India-462003.Department of Mathematics Maulana Azad National Institute of Technology, Bhopal, M.P. India-462003.The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces. In this article, the imposed hypotheses is amiable than the well-known Lipschitz and Hölder continuity conditions. The R-order convergence of the considered scheme is proved to be at least 4+3q. An approximate apriori error bound for this method is also elaborated and the domain of existence and uniqueness of the solution in the convergence theorem. Two numerical illustrations have been worked out to exhibit the virtue of the developed theory.http://www.utgjiu.ro/math/sma/v15/p15_12.pdfbanach spacesemi-local convergenceω-continuity conditionr-order of convergenceerror bound |
| spellingShingle | Neha Gupta Jai Prakash Jaiswal SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION Surveys in Mathematics and its Applications banach space semi-local convergence ω-continuity condition r-order of convergence error bound |
| title | SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION |
| title_full | SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION |
| title_fullStr | SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION |
| title_full_unstemmed | SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION |
| title_short | SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION |
| title_sort | semi local convergence of a seventh order method in banach spaces under ω continuity condition |
| topic | banach space semi-local convergence ω-continuity condition r-order of convergence error bound |
| url | http://www.utgjiu.ro/math/sma/v15/p15_12.pdf |
| work_keys_str_mv | AT nehagupta semilocalconvergenceofaseventhordermethodinbanachspacesunderōcontinuitycondition AT jaiprakashjaiswal semilocalconvergenceofaseventhordermethodinbanachspacesunderōcontinuitycondition |