Abstract

In this paper, we introduce and consider a new class of variational inequalities which is called the mixed extended general bifunction variational inequality. We suggest and analyze some proximal methods for solving the mixed extended general 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.

Key words: General variational inequality, implicit method, convergence, auxiliary principle technique.