A Fixed Point Scheme for Nonexpansive Mappings, Variational Inequalities and Equilibrium Problems
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The purpose of this paper is to introduce a new iteration scheme and prove a strong convergence theorem for finding a common element of the fixed point set of a nonexpansive mapping, the solution set of variational inequalities and the solution set of equilibrium problems. Under certain conditions on parameters, we show that the iterative sequences generated by the scheme strongly converge to a common element in a real Hilbert space.
KeywordsNonexpansive Pseudomonotone Continuous Fixed point Variational inequalities Equilibrium problems
Mathematics Subject Classification (2000)65K10 90C33
This work is supported by the Vietnam Institute for Advanced Study in Mathematics.
We are very grateful to two anonymous referees for their really helpful and constructive comments on improving the paper.
- 19.Wangkeeree, R., Preechasilp, P.: A new iterative scheme for solving the equilibrium problems, variational inequality problems, and fixed point problems in Hilbert spaces. J. Appl. Math. 154968 (2012). 21 pp. doi: 10.1155/2012/154968