Orlicz dual of log-Aleksandrov–Fenchel inequality

Abstract

In this paper, we establish an Orlicz dual of the log-Aleksandrov–Fenchel inequality, by introducing two new concepts of dual mixed volume measures, and using the newly established Orlicz dual Aleksandrov–Fenchel inequality. The Orlicz dual log-Aleksandrov– Fenchel inequality in special cases yields the classical dual Aleksandrov–Fenchel inequality and some dual logarithmic Minkowski type inequalities, respectively. Moreover, the dual log-Aleksandrov–Fenchel inequality is therefore also derived.