Abstract

In this paper, we use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of equilibrium problems and variational inequalities, which is called the trifunction equilibrium variational inequality. Convergence of these iterative methods is proved under very mild and suitable assumptions. Several special cases are also considered. Results proved in this paper continue to hold for these known and new classes of equilibrium and variational inequalities.

Key words: Mixed variational inequality, equilibrium problems, convergence, auxiliary principle technique.