Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11493
Title: A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization
Authors: Chang, SS
Lee, HWJ 
Chan, CK 
Keywords: α-inverse-strongly monotone mapping
A family of infinitely nonexpansive mappings
Equilibrium problem
Fixed point
Viscosity approximation method
Issue Date: 2009
Publisher: Pergamon Press
Source: Nonlinear analysis : theory, methods and applications, 2009, v. 70, no. 9, p. 3307-3319 How to cite?
Journal: Nonlinear analysis : theory, methods and applications 
Abstract: In this paper, we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications, at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings. The results presented in the paper extend and improve some recent results of Yao and Yao [Y.Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput. 186 (2) (2007) 1551-1558], Plubtieng and Punpaeng [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings, Appl. Math. Comput. (2007) doi:10.1016/j.amc.2007.07.075], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for Equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2006) 506-515], Su, Shang and Qin [Y.F. Su, M.J. Shang, X.L. Qin, An iterative method of solution for equilibrium and optimization problems, Nonlinear Anal. (2007) doi:10.1016/j.na.2007.08.045] and Chang, Cho and Kim [S.S. Chang, Y.J. Cho, J.K. Kim, Approximation methods of solutions for equilibrium problem in Hilbert spaces, Dynam. Systems Appl. (in print)].
URI: http://hdl.handle.net/10397/11493
ISSN: 0362-546X
DOI: 10.1016/j.na.2008.04.035
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