The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems
The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fi...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/378750 |
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| author | Lu-Chuan Ceng Himanshu Gupta Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Himanshu Gupta Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | The purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of Fix(S)∩Ξ∩Γ under mild conditions. |
| format | Article |
| id | doaj-art-ee2ba79ec50649fbbb750c21730f4343 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ee2ba79ec50649fbbb750c21730f43432025-02-03T05:43:43ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/378750378750The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point ProblemsLu-Chuan Ceng0Himanshu Gupta1Ching-Feng Wen2Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Mathematics, Aligarh Muslim University, Aligarh 202 002, IndiaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanThe purpose of this paper is to introduce and analyze the Mann-type extragradient iterative algorithms with regularization for finding a common element of the solution set Ξ of a general system of variational inequalities, the solution set Γ of a split feasibility problem, and the fixed point set Fix(S) of a strictly pseudocontractive mapping S in the setting of the Hilbert spaces. These iterative algorithms are based on the regularization method, the Mann-type iteration method, and the extragradient method due to Nadezhkina and Takahashi (2006). Furthermore, we prove that the sequences generated by the proposed algorithms converge weakly to an element of Fix(S)∩Ξ∩Γ under mild conditions.http://dx.doi.org/10.1155/2013/378750 |
| spellingShingle | Lu-Chuan Ceng Himanshu Gupta Ching-Feng Wen The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems Abstract and Applied Analysis |
| title | The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems |
| title_full | The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems |
| title_fullStr | The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems |
| title_full_unstemmed | The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems |
| title_short | The Mann-Type Extragradient Iterative Algorithms with Regularization for Solving Variational Inequality Problems, Split Feasibility, and Fixed Point Problems |
| title_sort | mann type extragradient iterative algorithms with regularization for solving variational inequality problems split feasibility and fixed point problems |
| url | http://dx.doi.org/10.1155/2013/378750 |
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