Some inequalities for asymmetric L_p-mean zonoids

Abstract

Based on the notion of L_p-mean zonoids which is introduced by Xi, Guo and Leng, we define the notion of asymmetric L_p-mean zonoids and establish its an affine inequality. Further, we give the extremal values for volume, quermassintegrals of this notion and dual quermassintegrals of polar of this notion. Finally, associated with p-radial mean bodies, two monotonic inequalities for the asymmetric L_p-mean zonoids are obtained.