Orlicz log-Minkowski inequality

Abstract

In this paper, the well-known log-Minkowski inequality is extended to the Orlicz space. We first propose and establish an Orlicz logarithmic Minkowski inequality by introducing two new concepts of mixed volume measure and Orlicz mixed volume measure, and using the Orlicz Minkowski inequality for the mixed volumes. The Orlicz logarithmic Minkowski inequality in special case yields the Stancu's logarithmic Minkowski inequality. The Lp-mixed volume measure and Lp-logarithmic Minkowski inequality is first derived here, too.