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Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems. (English) Zbl 1171.90542

Summary: A new iterative scheme based on the extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a family of finitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Applications to optimization problems are given.

MSC:

90C47 Minimax problems in mathematical programming
65J15 Numerical solutions to equations with nonlinear operators
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