Construction of a common solution of a finite family of variational inequality problems for monotone mappings
Mohammed Alghamdi, Naseer Shahzad, Habtu Zegeye · The Journal of Nonlinear Sciences and Applications · 2016
Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let \(A_i : C \rightarrow H\), for \(i = 1; 2\); be two \(L_i\)-Lipschitz monotone mappings and let \(f : C \rightarrow C\) be a contraction mapping. It is our purpose in this paper to introduce an iterative process for finding a point in \(V I(C;A_1) \cap V I(C;A_2) \)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.