Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

We introduce an iterative algorithm for finding a common element of the set of fixed points for an infinite family of nonexpansive mappings, the set of solutions of the variational inequalities for a family of -inverse-strongly monotone mappings and the setof solutions of a system of equilibrium problems 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. Moreover, weapply our result to the problem of finding a common fixed point of a family of strictly pseudocontractive mappings.