General algorithm of solutions for nonlinear variational inequalities in Banach space

Abstract

In this paper, we shall study a class of general nonlinear variational inequalities in reflexive Banach spaces. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved. Next, by applying the auxiliary problem technique, we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality. Finally, the convergence criteria is also discussed.