On Inherited Properties for Vector-Valued Multifunctions

In this paper, we consider several kinds of convexity and semicontinuity of multifunctions with respect to ordering cones, and we investigate inherited properties of convexity and semicontinuity through scalarization of multifunctions. We introduce four kinds of scalarizing functions to characterize images of a multifunction by using Tchebyshev scalarization; these (real-valued) scalarizing functions have the same sorts of convexity and semicontinuity which correspond to those of parent multifunctions.