SOME INEQUALITIES FOR THE (p,q)-MIXED AFFINE SURFACE AREAS1

Weidong Wang ∗ Xia Zhao

Abstract. The notion of (p,q)-mixed volume was first introduced by Lutwak, Yang and Zhang in 2018. According to this concept, Li, Wang and Zhou defined the (p,q)-mixed affine surface areas in 2019. In this paper, we establish some inequalities including cyclic inequality, monotonous inequality and product inequality for the (p,q)-mixed affine surface areas.

Key words: (p,q)-mixed volume, (p,q)-mixed affine surface area, cyclic inequality, mo-notonous inequality, product inequality.