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http://dx.doi.org/10.14317/jami.2011.29.3_4.621

A GENERAL ITERATIVE ALGORITHM COMBINING VISCOSITY METHOD WITH PARALLEL METHOD FOR MIXED EQUILIBRIUM PROBLEMS FOR A FAMILY OF STRICT PSEUDO-CONTRACTIONS  

Jitpeera, Thanyarat (Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi(KMUTT))
Inchan, Issara (Department of Mathematics and Computer, Uttaradit Rajabhat University)
Kumam, Poom (Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi(KMUTT))
Publication Information
Journal of applied mathematics & informatics / v.29, no.3_4, 2011 , pp. 621-639 More about this Journal
Abstract
The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.
Keywords
strictly pseudo-contractions; mixed equilibrium problems; minimization problem; parallel method;
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