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Viscosity approximation methods for generalized equilibrium problems and fixed point problems with applications. (English) Zbl 1225.47106
Summary: We introduce a general iterative scheme for finding a common element of the set of common solutions of generalized equilibrium problems and the set of common fixed points of a family of infinite nonexpansive mappings. Strong convergence theorems are established in a real Hilbert space under suitable conditions. As applications, we consider convex feasibility problems and equilibrium problems. The results presented improve and extend the corresponding results of many others.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47N10Applications of operator theory in optimization, convex analysis, programming, economics
91B50General equilibrium theory in economics
47J20Inequalities involving nonlinear operators