Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems
We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strong...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/174796 |
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| _version_ | 1849305164511444992 |
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| author | Kriengsak Wattanawitoon Poom Kumam |
| author_facet | Kriengsak Wattanawitoon Poom Kumam |
| author_sort | Kriengsak Wattanawitoon |
| collection | DOAJ |
| description | We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors. |
| format | Article |
| id | doaj-art-03c1a5e8b130425591610db6e8fcf4d7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-03c1a5e8b130425591610db6e8fcf4d72025-08-20T03:55:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/174796174796Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium ProblemsKriengsak Wattanawitoon0Poom Kumam1Department of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Tak, Tak 63000, ThailandCentre of Excellence in Mathematics, CHE, Si Ayuthaya Road, Bangkok 10400, ThailandWe prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.http://dx.doi.org/10.1155/2011/174796 |
| spellingShingle | Kriengsak Wattanawitoon Poom Kumam Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems International Journal of Mathematics and Mathematical Sciences |
| title | Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems |
| title_full | Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems |
| title_fullStr | Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems |
| title_full_unstemmed | Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems |
| title_short | Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems |
| title_sort | hybrid proximal point methods for zeros of maximal monotone operators variational inequalities and mixed equilibrium problems |
| url | http://dx.doi.org/10.1155/2011/174796 |
| work_keys_str_mv | AT kriengsakwattanawitoon hybridproximalpointmethodsforzerosofmaximalmonotoneoperatorsvariationalinequalitiesandmixedequilibriumproblems AT poomkumam hybridproximalpointmethodsforzerosofmaximalmonotoneoperatorsvariationalinequalitiesandmixedequilibriumproblems |