This paper concerns explicitly quasiconvex set-valued maps,defined on a nonempty convex subset of a real linear space with values in a partially ordered real linear space, with respect to a solid vectorially closed convex cone. It is shown that these generalized convex set-valued maps can be...

This paper is focused on approximate ( $$\varepsilon$$ -efficient) solutions of multiobjective mathematical programs. We introduce a new $$\varepsilon$$ -efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these...

The aim of this paper is to characterize in terms of classical convexity and quasiconvexity of extended real-valued functions those set-valued maps which are K-convex or K-quasiconvex with respect to a convex cone K. In particular, we recover some known characterizations of K-convex and...