The Orlicz mean zonoid operator

Abstract In this paper, we introduce an Orlicz mean zonoid operator Z ϕ : ( K n ) 2 → K n which has Zhang's mean zonoid operator as a special case. We show that the new operator which actually maps ( K n ) 2 to K 0 n is commutative, GL ( n ) covariant and continuous. We also establish an affine isoperimetric inequality for the Orlicz mean zonoid.