Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem
We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly m...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/538912 |
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| _version_ | 1832561026119237632 |
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| author | Tanom Chamnarnpan Poom Kumam |
| author_facet | Tanom Chamnarnpan Poom Kumam |
| author_sort | Tanom Chamnarnpan |
| collection | DOAJ |
| description | We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part. |
| format | Article |
| id | doaj-art-83e57d2e017d4147ad61a37deca8fc72 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-83e57d2e017d4147ad61a37deca8fc722025-02-03T01:26:07ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/538912538912Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization ProblemTanom Chamnarnpan0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, ThailandWe introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.http://dx.doi.org/10.1155/2012/538912 |
| spellingShingle | Tanom Chamnarnpan Poom Kumam Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem Journal of Applied Mathematics |
| title | Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem |
| title_full | Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem |
| title_fullStr | Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem |
| title_full_unstemmed | Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem |
| title_short | Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem |
| title_sort | iterative algorithms for solving the system of mixed equilibrium problems fixed point problems and variational inclusions with application to minimization problem |
| url | http://dx.doi.org/10.1155/2012/538912 |
| work_keys_str_mv | AT tanomchamnarnpan iterativealgorithmsforsolvingthesystemofmixedequilibriumproblemsfixedpointproblemsandvariationalinclusionswithapplicationtominimizationproblem AT poomkumam iterativealgorithmsforsolvingthesystemofmixedequilibriumproblemsfixedpointproblemsandvariationalinclusionswithapplicationtominimizationproblem |