Generalized mixed quasi trifunction variational inequalities

In this paper, we introduce a new class of trifunction variational inequalities, which is called the generalized mixed quasi trifunction variational inequalities. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the generalized mixed quasi trifunction variational inequalities. It is shown that the convergence of the proposed method requires only pseudomonotonicity, which is a weaker condition than monotonicity. Our results represent an improvement and refinement of previously known results. Since the generalized mixed quasi trifunction variational inequalities include bifunction variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.