Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces
The purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being also zeros of an m-accretive operator A in the setting of real uniformly convex and 2-uniformly smooth Banach space X. Here the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/852760 |
| _version_ | 1798046106006847488 |
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| author | Lu-Chuan Ceng Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | The purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being
also zeros of an m-accretive operator A in the setting of real uniformly convex and 2-uniformly
smooth Banach space X. Here the modified hybrid steepest-descent methods are based on
Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descent
algorithms for finding a common element of the solution set of the GSVI and the set A-1(0) of zeros of A in X. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the
corresponding results announced in the earlier and very recent literature. |
| first_indexed | 2024-04-11T23:32:08Z |
| format | Article |
| id | doaj.art-1e3d00a97b9d4036abc75c584d410c4c |
| institution | Directory Open Access Journal |
| issn | 1085-3375 1687-0409 |
| language | English |
| last_indexed | 2024-04-11T23:32:08Z |
| publishDate | 2013-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj.art-1e3d00a97b9d4036abc75c584d410c4c2022-12-22T03:57:05ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/852760852760Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach SpacesLu-Chuan Ceng0Ching-Feng Wen1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanThe purpose of this paper is to introduce and analyze modified hybrid steepest-descent methods for a general system of variational inequalities (GSVI), with solutions being also zeros of an m-accretive operator A in the setting of real uniformly convex and 2-uniformly smooth Banach space X. Here the modified hybrid steepest-descent methods are based on Korpelevich's extragradient method, hybrid steepest-descent method, and viscosity approximation method. We propose and consider modified implicit and explicit hybrid steepest-descent algorithms for finding a common element of the solution set of the GSVI and the set A-1(0) of zeros of A in X. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.http://dx.doi.org/10.1155/2013/852760 |
| spellingShingle | Lu-Chuan Ceng Ching-Feng Wen Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces Abstract and Applied Analysis |
| title | Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces |
| title_full | Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces |
| title_fullStr | Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces |
| title_full_unstemmed | Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces |
| title_short | Modified Hybrid Steepest-Descent Methods for General Systems of Variational Inequalities with Solutions to Zeros of m-Accretive Operators in Banach Spaces |
| title_sort | modified hybrid steepest descent methods for general systems of variational inequalities with solutions to zeros of m accretive operators in banach spaces |
| url | http://dx.doi.org/10.1155/2013/852760 |
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