A generalized vector variational inequality problem with a set-valued semi-monotone mapping

In this paper, we first generalize the concept of semi-monotonicity for a scalar single-valued mapping to the case of a vector set-valued mapping. Then we consider a generalized vector variational inequality problem concerning the vector set-valued semi-monotone mapping; several existence results are obtained by using the Kakutani–Fan–Glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years.