Strong convergence theorems for an infinite family of quasi-nonexpansive mappings and generalized equilibrium problems and variational inequality problems

In this paper, we introduce a new iterative scheme for finding a common element of the set of common fixed points of an infinite family of uniformly continuous quasi-nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three mentioned sets. Our results extend important recent results.