General equilibrium bifunction variational inequalities

In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximal methods for solving mixed general equilibrium bifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under some mild suitable conditions. Several cases are also discussed. Results in this paper include some new and known results as special cases.