SOME CHARACTERIZATIONS FOR VECTOR VARIATIONAL-LIKE INEQUALITIES

Abstract

In this paper, a class of $\eta$-PPM mappings $F$ where $F$ and $-F$ are both $\eta$-pseudomonotone are introduced, which are proper generalizations of the PPM mappings considered by Bianchi and Schaible. The solution sets of two kinds of vector variational-like inequality problems involving $\eta$-PPM mappings are characterized in Banach spaces. Furthermore, the solution sets of two classes of vector variational-like inequalities involving set-valued mappings are also characterized via the scalarization approach due to Konnov.