On a general projection algorithm for variational inequalities involving relaxed Lipschitz and relaxed monotone mappings

Abstract

In this paper, we consider the generalized nonlinear quasi-variational inequalities problem for set-valued mappings and construct an iterative algorithm for find the approximate solution of this problem by exploiting the projection method and prove the existence of the solution to our problem involving relaxed Lipschitz and relaxed monotone mappings and the convergence of the iterative sequences generated by this algorithm.