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We introduce a new iterative scheme by hybrid method for finding acommon element of the set of common fixed points of infinite family of nonexpansive mappings,the set of common solutions to a system of generalized mixed equilibrium problems, and theset of solutions to a variational inequality problem in a real Hilbert space. We then prove strongconvergence of the scheme to a common element of the three sets. We give some applications ofour results. Our results extend important recent results

international journal of mathematics and mathematical sciences

Strong Convergence Theorems for Family of Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems