Abstract : This paper introduces a local non-positivity of two set-valued mappings $(F,Q)$ and considers the existences and properties of solutions for set-valued mixed vector $FQ$-implicit variational inequality problems and set-valued mixed vector $FQ$-complementarity problems in the neighborhood of a point belonging to an underlined domain $K$ of the set-valued mappings, where the neighborhood is contained in $K$. This paper generalizes and extends many results in [1, 3-7].
