Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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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))
  • Received : 2010.01.10
  • Accepted : 2010.05.20
  • Published : 2011.01.30
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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

Acknowledgement

Supported by : King Mongkut's University of Technology Thonburi

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