Existence Results for Variational Inequalities with Surjectivity Consequences Related to Generalized Monotone Operators
We present existence results for variational inequalities given by generalized monotone operators. As a consequence, we deduce the existence of zeros, or even more, the surjectivity of some classes of set-valued operators. We show that by strengthening the continuity assumptions, similar surjectivity results can be obtained without any monotonicity assumption. In the framework of reflexive Banach spaces, we extend a related result due to Inoan and Kolumbn (Nonlinear Anal. 68:4753, 2008).
variational inequality equilibrium problem quasicoercive operator properly quasimonotone operator f-hemicontinuity c-pseudomonotone operator