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Extragradient method for equilibrium problems and variational inequalities. (English) Zbl 1205.47063
Summary: In this paper, we suggest and analyze a new extragradient method for finding a common element of the set of solutions of an equilibrium problem, the set of fixed points of a nonexpansive mapping, and the set of solutions of some variational inequality. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our result includes the main result of A. Bnouhachem, M. A. Noor and Z. Hao [Nonlinear Anal., Theory Methods Appl. 70, No. 3 (A), 1321–1329 (2009; Zbl 1171.47050)] as a special case.

47J25 Iterative procedures involving nonlinear operators
47H10 Fixed-point theorems
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics