Generalized mixed quasi-equilibrium problems with trifunction

In this paper, we introduce a new class of equilibrium problems, which is called the generalized mixed quasi-equilibrium problems with trifunction. Using the auxiliary principle technique, we suggest and analyze a proximal point method for solving the generalized mixed quasi-equilibrium problems. 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-equilibrium problems include equilibrium problems and variational inequalities as special cases, results proved in this paper continue to hold for these problems.