Cyclic inequalities for generalized mixed width-integrals

Abstract

In this paper, we research the cyclic inequalities of generalized width-integral in convex geometry analysis. Based on previous studies, we use Hölder’s inequality and inverse Hölder’s inequality to study further the generalized width-integral inequalities of the convex body in Euclidean space, establish a series of cyclic inequalities, and give the condition of equality sign.