A Newton-type method and its application
We prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) an...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/23674 |
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| _version_ | 1832555051597430784 |
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| author | V. Antony Vijesh P. V. Subrahmanyam |
| author_facet | V. Antony Vijesh P. V. Subrahmanyam |
| author_sort | V. Antony Vijesh |
| collection | DOAJ |
| description | We prove an existence and uniqueness theorem for solving the
operator equation F(x)+G(x)=0, where F
is a continuous and
Gâteaux differentiable operator and the operator G
satisfies
Lipschitz condition on an open convex subset of a Banach space. As
corollaries, a recent theorem of Argyros (2003) and the classical
convergence theorem for modified Newton iterates are deduced. We
further obtain an existence theorem for a class of nonlinear
functional integral equations involving the Urysohn operator. |
| format | Article |
| id | doaj-art-650e8833b5804ec8bb581e477101c9d8 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-650e8833b5804ec8bb581e477101c9d82025-02-03T05:49:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/2367423674A Newton-type method and its applicationV. Antony Vijesh0P. V. Subrahmanyam1Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, IndiaDepartment of Mathematics, Indian Institute of Technology Madras, Chennai 600036, IndiaWe prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. We further obtain an existence theorem for a class of nonlinear functional integral equations involving the Urysohn operator.http://dx.doi.org/10.1155/IJMMS/2006/23674 |
| spellingShingle | V. Antony Vijesh P. V. Subrahmanyam A Newton-type method and its application International Journal of Mathematics and Mathematical Sciences |
| title | A Newton-type method and its application |
| title_full | A Newton-type method and its application |
| title_fullStr | A Newton-type method and its application |
| title_full_unstemmed | A Newton-type method and its application |
| title_short | A Newton-type method and its application |
| title_sort | newton type method and its application |
| url | http://dx.doi.org/10.1155/IJMMS/2006/23674 |
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