The existence of contingent epiderivative for a set-valued mapping and vector variational-like inequalities

Abstract

In this paper we analyze the existence of the contingent epiderivative for a set-valued mapping in a general normed space with respect to Daniell cone. As its application, we will also establish the relationships between set-valued optimization problems and variational-like inequality problems under the conditions of pseudo invexity. MSC: 49J52; 90C56