Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities
We introduce new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequenc...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/153456 |
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| _version_ | 1832550375424524288 |
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| author | Jong Soo Jung |
| author_facet | Jong Soo Jung |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | We introduce new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k-strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum-norm fixed point of a k-strictly pseudocontractive mapping. |
| format | Article |
| id | doaj-art-c0ea57e18a5346a098e3069c0a9c2747 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c0ea57e18a5346a098e3069c0a9c27472025-02-03T06:07:02ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/153456153456Some Algorithms for Finding Fixed Points and Solutions of Variational InequalitiesJong Soo Jung0Department of Mathematics, Dong-A University, Busan 604-714, Republic of KoreaWe introduce new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k-strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum-norm fixed point of a k-strictly pseudocontractive mapping.http://dx.doi.org/10.1155/2012/153456 |
| spellingShingle | Jong Soo Jung Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities Abstract and Applied Analysis |
| title | Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities |
| title_full | Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities |
| title_fullStr | Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities |
| title_full_unstemmed | Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities |
| title_short | Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities |
| title_sort | some algorithms for finding fixed points and solutions of variational inequalities |
| url | http://dx.doi.org/10.1155/2012/153456 |
| work_keys_str_mv | AT jongsoojung somealgorithmsforfindingfixedpointsandsolutionsofvariationalinequalities |