A NECESSARY AND SUFFICIENT CONDITION FOR UPPER HEMICONTINUOUS SET-VALUED MAPPINGS WITHOUT COMPACT-VALUES BEING UPPER DEMICONTINUOUS

The purpose of this article is to give a characterization of an upper hemicontinuous mapping with non-empty convex values being upper demico ntinuous, i.e., we show that an upper hemicontinuous set-valued mappin g with non-empty convex values (not necessarily compact-valued) is upp er demicontinuous if and only if the set-valued mapping has no interio r asymptotic plane.