A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of stri...

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Published inJournal of Applied Mathematics Vol. 2012; no. 2012; pp. 1007 - 1021-660
Main Authors Wang, Yaqin, Fang, Xiaoli, Xu, Hong Kun
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Convergence
Hilbert space
Inequalities
Inequality
Iterative algorithms
Iterative methods
Mapping
Mathematical analysis
Methods
Optimization
Studies
Theorems
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Abstract The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others.
AbstractList The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others.
Author Hongkun Xu
Xiaoli Fang
Yaqin Wang
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10.1016/j.nahs.2009.02.007
10.11650/twjm/1500405033
10.11650/twjm/1500407345
10.1007/s12190-008-0129-1
10.1016/j.aml.2010.12.048
10.1016/j.na.2008.04.035
10.1016/j.na.2008.02.014
10.1016/j.cam.2007.02.022
10.1090/S0002-9947-1970-0282272-5
10.1016/j.nahs.2008.09.017
10.1016/j.nahs.2010.10.005
10.1016/j.na.2007.05.032
10.1007/s10898-009-9454-7
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Copyright Copyright © 2012 Yaqin Wang et al.
Copyright © 2012 Yaqin Wang et al. Yaqin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright Hindawi Publishing Corporation
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SubjectTerms Convergence
Hilbert space
Inequalities
Inequality
Iterative algorithms
Iterative methods
Mapping
Mathematical analysis
Methods
Optimization
Studies
Theorems
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Title A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings
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