Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems
We introduce two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium...
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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/10.1155/2014/436069 |
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| _version_ | 1832549256107393024 |
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| author | Lu-Chuan Ceng Juei-Ling Ho |
| author_facet | Lu-Chuan Ceng Juei-Ling Ho |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | We introduce two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inequalities for inverse strong monotone mappings and the set of fixed points of an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under mild conditions. |
| format | Article |
| id | doaj-art-b412c497b64449aaa624620a519be888 |
| 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-b412c497b64449aaa624620a519be8882025-02-03T06:11:47ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/436069436069Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point ProblemsLu-Chuan Ceng0Juei-Ling Ho1Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Finance, Tainan University of Technology, No. 529, Zhongzheng Road, YongKang District, Tainan 71002, TaiwanWe introduce two iterative algorithms by the hybrid extragradient method with regularization for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of finite generalized mixed equilibrium problems, the set of solutions of finite variational inequalities for inverse strong monotone mappings and the set of fixed points of an asymptotically κ-strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under mild conditions.http://dx.doi.org/10.1155/2014/436069 |
| spellingShingle | Lu-Chuan Ceng Juei-Ling Ho Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems Abstract and Applied Analysis |
| title | Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems |
| title_full | Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems |
| title_fullStr | Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems |
| title_full_unstemmed | Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems |
| title_short | Hybrid Extragradient Method with Regularization for Convex Minimization, Generalized Mixed Equilibrium, Variational Inequality and Fixed Point Problems |
| title_sort | hybrid extragradient method with regularization for convex minimization generalized mixed equilibrium variational inequality and fixed point problems |
| url | http://dx.doi.org/10.1155/2014/436069 |
| work_keys_str_mv | AT luchuanceng hybridextragradientmethodwithregularizationforconvexminimizationgeneralizedmixedequilibriumvariationalinequalityandfixedpointproblems AT jueilingho hybridextragradientmethodwithregularizationforconvexminimizationgeneralizedmixedequilibriumvariationalinequalityandfixedpointproblems |