The dual affine log-Minkowski inequality

Abstract

UDC 517.98, 514.17

We deduce an affine dual log-Minkowski inequality by introducing two new concepts of dual affine measure and Orlicz dual affine measure and using the newly established Orlicz dual affine Minkowski inequality. In a special case, the Orlicz affine dual log-Minkowski inequality  yields the $L_{p}$-affine dual log-Minkowski inequality. The affine dual log-Minkowski inequality is also obtained.