Vector implicit quasi complementarity problems

In this work, we establish some existence theorems for solutions to a new class of vector implicit quasi complementarity problems and the corresponding vector implicit quasi variational inequality problems. Further we introduce the notion of a local non-positivity of a pair of mappings (F, Q) and consider the existence and properties of solutions for vector implicit quasi variational inequality problems and the corresponding vector implicit quasi complementarity problems in the neighborhood of a given point belonging to an underlined domain K.