A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems
The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/206345 |
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| author | Uamporn Witthayarat Thanyarat Jitpeera Poom Kumam |
| author_facet | Uamporn Witthayarat Thanyarat Jitpeera Poom Kumam |
| author_sort | Uamporn Witthayarat |
| collection | DOAJ |
| description | The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part. |
| format | Article |
| id | doaj-art-710abf0235864fafaa800aac90e26fce |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-710abf0235864fafaa800aac90e26fce2025-02-03T05:43:54ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/206345206345A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization ProblemsUamporn Witthayarat0Thanyarat Jitpeera1Poom Kumam2Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi KMUTT, Bangkok 10140, ThailandDepartment of Mathematics and Statistics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna Chiang Rai, Chiang Rai 57120, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi KMUTT, Bangkok 10140, ThailandThe purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.http://dx.doi.org/10.1155/2012/206345 |
| spellingShingle | Uamporn Witthayarat Thanyarat Jitpeera Poom Kumam A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems Abstract and Applied Analysis |
| title | A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems |
| title_full | A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems |
| title_fullStr | A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems |
| title_full_unstemmed | A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems |
| title_short | A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems |
| title_sort | new modified hybrid steepest descent by using a viscosity approximation method with a weakly contractive mapping for a system of equilibrium problems and fixed point problems with minimization problems |
| url | http://dx.doi.org/10.1155/2012/206345 |
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