A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems
We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the generalized mi...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/123027 |
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| _version_ | 1850159473978507264 |
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| author | Siwaporn Saewan Poom Kumam |
| author_facet | Siwaporn Saewan Poom Kumam |
| author_sort | Siwaporn Saewan |
| collection | DOAJ |
| description | We introduce a new hybrid iterative scheme for finding a common element of the set
of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set
of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the
generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a
real Banach space. We obtain a strong convergence theorem for the sequences generated by this process
in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve
and extend some recent results. |
| format | Article |
| id | doaj-art-b4c2e5c13d14409aadeee97dc06eb01e |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b4c2e5c13d14409aadeee97dc06eb01e2025-08-20T02:23:31ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/123027123027A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality ProblemsSiwaporn Saewan0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandWe introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.http://dx.doi.org/10.1155/2010/123027 |
| spellingShingle | Siwaporn Saewan Poom Kumam A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems Abstract and Applied Analysis |
| title | A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems |
| title_full | A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems |
| title_fullStr | A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems |
| title_full_unstemmed | A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems |
| title_short | A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems |
| title_sort | hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi nonexpansive mappings for generalized mixed equilibrium and variational inequality problems |
| url | http://dx.doi.org/10.1155/2010/123027 |
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