Abstract
In this paper we introduce a new iterative process for finding a common element of the set of solutions of monotone and Lipschitz-type continuous Ky Fan inequality and the common fixed points of an infinite family of quasi-nonexpansive mappings in a real Hilbert space. We establish a strong convergence for an iterative process to find a unique solution of the variational inequality which is the optimality condition for the minimization problem. Our results generalize and improve some known results.