The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems
In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α -inverse-str...
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| Abstract | In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi -
ϕ
- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an
α
-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. |
|---|---|
| AbstractList | In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α -inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - - asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an [alpha]-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature.ABSTRACTIn this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Moreover, we obtain a strong convergence theorem for the sequence generated by this process in the framework Banach spaces. The results presented in this paper improve and generalize some well-known results in the literature. |
| ArticleNumber | 8 |
| Author | Saewan, Siwaporn Kumam, Poom |
| Author_xml | – sequence: 1 givenname: Siwaporn surname: Saewan fullname: Saewan, Siwaporn organization: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) – sequence: 2 givenname: Poom surname: Kumam fullname: Kumam, Poom email: poom.kum@kmutt.ac.th organization: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/23687626$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1155/2011/701675 10.1080/02331939608844225 10.1007/s12190-009-0330-x 10.1016/j.amc.2011.08.099 10.1155/2010/141376 10.1016/j.amc.2009.11.031 10.1016/j.jat.2005.02.007 10.1186/1687-1812-2011-9 10.1155/S1687182004310089 10.1155/2008/528476 10.1186/1029-242X-2011-96 10.1137/S105262340139611X 10.1016/j.cam.2008.06.011 10.1016/j.amc.2010.02.054 10.1090/S0002-9947-1970-0282272-5 10.1016/j.na.2008.03.058 10.1155/2008/312454 10.1016/j.jmaa.2007.07.019 10.1186/1687-1812-2011-104 10.1016/j.na.2007.11.031 10.1016/0022-247X(83)90112-9 10.1007/s12190-009-0230-0 10.1016/j.na.2009.10.014 10.1515/JAA.2001.151 10.1007/s12190-008-0129-1 10.1016/j.camwa.2011.06.014 10.1186/1687-1812-2011-35 10.1155/2008/284613 10.1081/NFA-120023869 10.1137/070688717 10.1016/j.nahs.2008.10.002 |
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| Keywords | A system of equilibrium problem 47H10 Hybrid block iterative algorithm Variational inequality 47H09 Inverse-strongly monotone operator Uniformly quasi asymptotically nonexpansive mapping 47H05 Uniformly quasi- ϕ-asymptotically nonexpansive mapping |
| Language | English |
| License | http://creativecommons.org/licenses/by/2.0 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| Title | The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems |
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