Solutions of system of equilibrium and variational inequality problems on fixed points of infinite family of nonexpansive mappings

In this paper, we introduce a hybrid viscosity approximation scheme for finding a common element of the solution set for a system of equilibrium problems, the solution set for a system of variational inequality problems and the common fixed point set for an infinite family of nonexpansive mappings in Hilbert spaces. Then we prove the strong convergence of the proposed iterative scheme. Our results improve and extend the results announced by Ceng and Yao (2008) [4].