DIFFERENCE INEQUALITIES FOR THE i-TH MIXED AFFINE SURFACE AREAS

XIA ZHAO 1 , WEIDONG WANG 2,∗

1 Department of Mathematics, China Three Gorges University, Yichang, China

2 Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, China

Abstract. Lutwak introduced the notion of i-th mixed affine surface areas and Leng defined the volume difference functions. In this paper, we establish difference inequalities of Brunn-Minkowski type and cycle type for i-th mixed affine surface areas. In particular, we obtain the Minkowski type inequality for the difference of i-th mixed affine surface areas.

Keywords. i-th mixed affine surface area; Difference; Brunn-Minkowski inequality; Cycle inequality; Minkowski inequality.