Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems
We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimizatio...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/637324 |
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| _version_ | 1832567033748783104 |
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| author | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | We first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions. |
| format | Article |
| id | doaj-art-4c39f22294274be5b36cddfa3ef604d7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4c39f22294274be5b36cddfa3ef604d72025-02-03T01:02:30ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/637324637324Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several ProblemsLu-Chuan Ceng0Cheng-Wen Liao1Chin-Tzong Pang2Ching-Feng Wen3Scientific Computing Key Laboratory of Shanghai Universities, Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Food and Beverage Management, Vanung University, Chung-Li 320061, TaiwanDepartment of Information Management, and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, TaiwanCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe first introduce and analyze one multistep iterative algorithm by hybrid shrinking projection method for finding a solution of the system of generalized equilibria with constraints of several problems: the generalized mixed equilibrium problem, finitely many variational inclusions, the minimization problem for a convex and continuously Fréchet differentiable functional, and the fixed-point problem of an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove strong convergence theorem for the iterative algorithm under suitable conditions. On the other hand, we also propose another multistep iterative algorithm involving no shrinking projection method and derive its weak convergence under mild assumptions.http://dx.doi.org/10.1155/2014/637324 |
| spellingShingle | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems Abstract and Applied Analysis |
| title | Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems |
| title_full | Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems |
| title_fullStr | Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems |
| title_full_unstemmed | Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems |
| title_short | Multistep Hybrid Iterations for Systems of Generalized Equilibria with Constraints of Several Problems |
| title_sort | multistep hybrid iterations for systems of generalized equilibria with constraints of several problems |
| url | http://dx.doi.org/10.1155/2014/637324 |
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