Existence results for Stampacchia and Minty type implicit variational inequalities with multivalued maps

Stampacchia and Minty type generalized implicit variational inequality problems are considered. We extended the notion of dense pseudomonotonicity for multivalued maps and established several existence results for solutions of these problems in the setting of segment-dense sets. We also studied the existence of solutions of Minty type generalized implicit quasi-variational inequality problems. Some particular cases are also studied. It is shown that our results contain several existing results in the literature as special cases.