Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces
The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. For semilocal convergence, the domain of the parameters is obtained to e...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/7352780 |
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| author | Abhimanyu Kumar Dharmendra K. Gupta Eulalia Martínez Sukhjit Singh |
| author_facet | Abhimanyu Kumar Dharmendra K. Gupta Eulalia Martínez Sukhjit Singh |
| author_sort | Abhimanyu Kumar |
| collection | DOAJ |
| description | The semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. For semilocal convergence, the domain of the parameters is obtained to ensure guaranteed convergence under suitable initial approximations. The applicability of local convergence is extended as the differentiability condition on the involved operator is avoided. The region of accessibility and a way to enlarge the convergence domain are provided. Theorems are given for the existence-uniqueness balls enclosing the unique solution. Finally, some numerical examples including nonlinear Hammerstein type integral equations are worked out to validate the theoretical results. |
| format | Article |
| id | doaj-art-147639b306cc4025a5ba8b11b13a536d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-147639b306cc4025a5ba8b11b13a536d2025-02-03T05:53:32ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/73527807352780Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach SpacesAbhimanyu Kumar0Dharmendra K. Gupta1Eulalia Martínez2Sukhjit Singh3Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaDepartment of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, IndiaInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, SpainDepartment of Mathematical Science, Punjab Technical University Jalandhar, Jalandhar, IndiaThe semilocal and local convergence analyses of a two-step iterative method for nonlinear nondifferentiable operators are described in Banach spaces. The recurrence relations are derived under weaker conditions on the operator. For semilocal convergence, the domain of the parameters is obtained to ensure guaranteed convergence under suitable initial approximations. The applicability of local convergence is extended as the differentiability condition on the involved operator is avoided. The region of accessibility and a way to enlarge the convergence domain are provided. Theorems are given for the existence-uniqueness balls enclosing the unique solution. Finally, some numerical examples including nonlinear Hammerstein type integral equations are worked out to validate the theoretical results.http://dx.doi.org/10.1155/2018/7352780 |
| spellingShingle | Abhimanyu Kumar Dharmendra K. Gupta Eulalia Martínez Sukhjit Singh Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces Complexity |
| title | Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces |
| title_full | Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces |
| title_fullStr | Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces |
| title_full_unstemmed | Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces |
| title_short | Convergence of a Two-Step Iterative Method for Nondifferentiable Operators in Banach Spaces |
| title_sort | convergence of a two step iterative method for nondifferentiable operators in banach spaces |
| url | http://dx.doi.org/10.1155/2018/7352780 |
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