In this paper, we introduce a general iterative algorithm for finding the common element of the set of common fixed points of an infinite family of nonexpansive mappings, the set of solutions of systems of equilibrium problems and the set of solutions of systems of variational inequalities for two strongly monotone mappings in a real Hilbert space. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions. Our results improve and extend the corresponding results announced by Colao and Marino [V. Colao and G. Marino, strong convergence for a minimization problem on points of equilibrium andcommonfixed points of an infinite family of nonexpansive mappings, Nonlinear Anal. (2010) 3513–3524] and many others.
