49J40,90C33.

In this paper, we use the auxiliary principle technique to suggest and analyze a predictor-corrector method for solving general mixed quasi variational inequalities. If the bifunction involving the mixed quasi variational inequalities is skew-symmetric , then it is shown that the convergence of the new method requires the partially relaxed strongly monotonicity of the operator, which is a weaker condition than cocoercivity. Since the general mixed quasi variational inequalities includes the classical quasi variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Our results can be viewed an important extension of the previously known results for variational inequalities.;