Abstract
In this paper, we introduce and consider a new class of variational inequalities, which is called the mixed quasi bifunction variational inequality. We use the auxiliary principle technique in conjunction with the Bregman function to suggest and analyze a three-step predictor-corrector method for solving mixed quasi bifunction variational inequalities. We also study the convergence criteria of this new method under some mild conditions. As special cases, we obtain various new and known methods for solving variational inequalities and related optimization problems.