Strong convergence for variational inequalities and equilibrium

We introduce an implicit method for nding a common element of the set of solutions of systems ofequilibrium problems and the set of common xed points of a sequence of nonexpansive mappings anda representation of nonexpansive mappings. then we prove the strong convergence of the proposedimplicit schemes to the unique solution of a variational inequality, which is the optimality conditionfor a minimization problem and is also a common xed point for a sequence of nonexpansive mappingsand a representation of nonexpansive mappings.