mixed quasi bifunction variational inequalities

In this paper, we introduce and study a new class of mixed quasi bifunction variational inequalities. we use the auxiliary principle technique in conjunction with the bregman function to suggest and analyze a two-step predictor-corrector method for solving mixed quasi variational inequalities involving bifunction. we also study the convergence criteria of this new method under some mild conditions. some special cases are also discussed. since mixed quasi variational inequalities involving the bifunction include several classes of variational inequalities and related optimization problems as special cases, results obtained in this paper continue to hold for these problems.