The Orlicz mean zonoid operator

In this paper, we introduce an Orlicz mean zonoid operator Zϕ:(Kn)2→KnZϕ:(Kn)2→Kn which has Zhang's mean zonoid operator as a special case. We show that the new operator which actually maps (Kn)2(Kn)2 to K0n is commutative, GL(n)GL(n) covariant and continuous. We also establish an affine isoperimetric inequality for the Orlicz mean zonoid.