Algorithm of solutions for mixed-nonlinear variational-like inequalities in reflexive banach space

In this paper, the author studies a class of mixed nonlinear variational-likeinequalities in reflexive Banach space. By applying a minimax inequality obtuined bythe author, some existence uniqueness theorems of solutions for foe mixed nonlinearvariational-like inequalities are proved. Next, by applying the applying the auxiliary problemtechnique, the author suggests an innovative iterative algorithm to compute theapproximate solutions of the mixed nonlinear variational-like inequalities. Finally theconvergence criteria is also discussed.