General mixed bifunction variational inequalities

Abstract

In this paper, we introduce and study some new classes of mixed bifunction variational inequalities. Some important special cases are discussed. The auxiliary principle technique is used to suggest and analyze a class of predictor-corrector methods for computing the fixed-points of general mixed bifunction variational inequalities. The convergence of the proposed methods only requires the partially relaxed monotonicity of the operator, which is weaker than co-coercivity and strongly monotonicity. As special cases, we obtain a number of known and new results for solving various classes of variational inequalities and related problems