Construction of a common solution of a finite family of variational inequality problems for monotone mappings

Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let A(i) : C -> H, for i = 1, 2, be two L-i-Lipschitz monotone mappings and let f : C -> C be a contraction mapping. It is our purpose in this paper to introduce an iterative process for finding a point in VI(C, A(1)) boolean AND VI(C, A(2)) under appropriate conditions. As a consequence, we obtain a convergence theorem for approximating a common solution of a finite family of variational inequality problems for Lipschitz monotone mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators. (C) 2016 All rights reserved.