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http://dx.doi.org/10.14317/jami.2011.29.1_2.227

A VISCOSITY APPROXIMATIVE METHOD TO CES$\`{A}$RO MEANS FOR SOLVING A COMMON ELEMENT OF MIXED EQUILIBRIUM, VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS  

Jitpeera, Thanyarat (Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT))
Katchang, Phayap (Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT))
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.1_2, 2011 , pp. 227-245 More about this Journal
Abstract
In this paper, we introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ${\beta}$inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Ces$\`{a}$ro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang [A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mapping, Nonlinear Analysis: Hybrid Systems, 3(2009), 475-86], Peng and Yao [Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems, Mathematical and Computer Modelling, 49(2009), 1816-828], Shimizu and Takahashi [Strong convergence to common fixed points of families of nonexpansive mappings, Journal of Mathematical Analysis and Applications, 211(1) (1997), 71-83] and some authors.
Keywords
Nonexpansive mapping; Fixed point; Variational inequality; Mixed equilibrium problem; Viscosity approximation method; Ces$\`{a}$ro mean approximation method;
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Times Cited By KSCI : 1  (Citation Analysis)
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