The Mixed Polar Orlicz-Brunn-Minkowski Inequalities

Abstract

Some Orlicz-Brunn-Minkowski type inequalities for (dual) quermassintegrals of polar bodies and star dual bodies have been introduced. In this paper, we generalize the results and establish some Orlicz-Brunn-Minkowski type inequalities for mixed (dual) quermassintegrals of polar bodies and star dual bodies.

Cyclic inequalities for generalized mixed width-integrals

“…Inspired by [2][3][4][5][6], this paper establishes a series of cyclic inequalities for width-integrals. The first established is the traditional circular inequality for the mixed width-integral.…”