Some Log-Minkowski Inequalities for (p, q)-Mixed Volume

Abstract

The notion of (p, q)-mixed volume was introduced by Lutwak, Yang and Zhang. In this paper, associated with the (p, q)-mixed volume, we prove a modification of the log-Minkowski inequality which is a unification form of the log-Minkowski inequality and the dual log-Minkowski inequality. As the application, we establish the (p, q)-mixed affine isoperimetric inequality.