Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities
We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational ine...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/280451 |
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| _version_ | 1832546527516557312 |
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| author | Muhammad Aslam Noor Khalida Inayat Noor Saira Zainab |
| author_facet | Muhammad Aslam Noor Khalida Inayat Noor Saira Zainab |
| author_sort | Muhammad Aslam Noor |
| collection | DOAJ |
| description | We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field. |
| format | Article |
| id | doaj-art-5521d74a921e4576b84922375dead77e |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5521d74a921e4576b84922375dead77e2025-02-03T06:48:35ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/280451280451Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational InequalitiesMuhammad Aslam Noor0Khalida Inayat Noor1Saira Zainab2Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, PakistanMathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, PakistanMathematics Department, HITEC University, Texila Cantt, Islamabad, PakistanWe introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.http://dx.doi.org/10.1155/2012/280451 |
| spellingShingle | Muhammad Aslam Noor Khalida Inayat Noor Saira Zainab Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities Journal of Applied Mathematics |
| title | Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities |
| title_full | Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities |
| title_fullStr | Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities |
| title_full_unstemmed | Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities |
| title_short | Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities |
| title_sort | some iterative methods for solving nonconvex bifunction equilibrium variational inequalities |
| url | http://dx.doi.org/10.1155/2012/280451 |
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