A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem
We introduce a new iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variation...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/562689 |
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| _version_ | 1850178832539058176 |
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| author | Atid Kangtunyakarn |
| author_facet | Atid Kangtunyakarn |
| author_sort | Atid Kangtunyakarn |
| collection | DOAJ |
| description | We introduce a new iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of fixed-point problems of infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of common fixed point of pseudocontractive mappings. |
| format | Article |
| id | doaj-art-c54fdf7cef824b3abcdc7074f7ba199d |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c54fdf7cef824b3abcdc7074f7ba199d2025-08-20T02:18:38ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/562689562689A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality ProblemAtid Kangtunyakarn0Department of Mathematics, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, ThailandWe introduce a new iterative scheme and a new mapping generated by infinite family of nonexpansive mappings and infinite real number. By using both of these ideas, we obtain strong convergence theorem for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of fixed-point problems of infinite family of nonexpansive mappings. Moreover, we apply our main result to obtain strong convergence theorems for finding a common element of the set of solution of equilibrium problem and the set of variational inequality and the set of common fixed point of pseudocontractive mappings.http://dx.doi.org/10.1155/2011/562689 |
| spellingShingle | Atid Kangtunyakarn A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem Abstract and Applied Analysis |
| title | A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem |
| title_full | A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem |
| title_fullStr | A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem |
| title_full_unstemmed | A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem |
| title_short | A New Iterative Algorithm for the Set of Fixed-Point Problems of Nonexpansive Mappings and the Set of Equilibrium Problem and Variational Inequality Problem |
| title_sort | new iterative algorithm for the set of fixed point problems of nonexpansive mappings and the set of equilibrium problem and variational inequality problem |
| url | http://dx.doi.org/10.1155/2011/562689 |
| work_keys_str_mv | AT atidkangtunyakarn anewiterativealgorithmforthesetoffixedpointproblemsofnonexpansivemappingsandthesetofequilibriumproblemandvariationalinequalityproblem AT atidkangtunyakarn newiterativealgorithmforthesetoffixedpointproblemsofnonexpansivemappingsandthesetofequilibriumproblemandvariationalinequalityproblem |