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An iterative method for finding common solutions of system of equilibrium problems and fixed point problems in Hilbert spaces

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a system of equilibrium problems and of the set of fixed points of a nonexpansive mapping in a Hilbert space. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Our results extend and generalize related work.