Some inequalities for asymmetric Lp-mean zonoids1

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.