Minkowski-Radstrom-Hormander Cone

Abstract

In this paper we introduce and investigate the notion of the generalized Minkowski-Radstrom Hormander cone giving a special attention to the order law of cancellation. In particular we embed the convex cone e(X) of nonempty closed convex subsets of real Hausdorff topological vector space and the convex cone W(R-n) of nonempty convex subsets of R-n into respective Minkowski-Radstrom-Hormander cones. We also prove the existence of minimal representation of elements of the MRH cone e(X) x K(X)/similar to (K(X) is the family of all compact convex subsets of X) and present reduction techniques for elements of the MRH cone e(X) x B(X)/similar to (B(X) is the family of all bounded closed convex subsets of X).