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http://dx.doi.org/10.14317/jami.2013.813

STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS OF QUASI-NONEXPANSIVE MAPPINGS AND VARIATIONAL INEQUALITY PROBLEMS  

Li, Meng (Department of Mathematics, Ordnance Engineering College)
Sun, Qiumei (Department of Mathematics, Ordnance Engineering College)
Zhou, Haiyun (Department of Mathematics, Ordnance Engineering College)
Publication Information
Journal of applied mathematics & informatics / v.31, no.5_6, 2013 , pp. 813-823 More about this Journal
Abstract
In this paper, a new iterative algorithm involving quasi-nonexpansive mapping in Hilbert space is proposed and proved to be strongly convergent to a point which is simultaneously a fixed point of a quasi-nonexpansive mapping, a solution of an equilibrium problem and the set of solutions of a variational inequality problem. The results of the paper extend previous results, see, for instance, Takahashi and Takahashi (J Math Anal Appl 331:506-515, 2007), P.E.Maing $\acute{e}$ (Computers and Mathematics with Applications, 59: 74-79,2010) and other results in this field.
Keywords
Equilibrium; Quasi-nonexpansive; Demiclosed; Variational inequality;
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