Orlicz version of the mixed width integrals

Abstract

In the paper, our main aim is to generalize the width integrals to the Orlicz space. Under the framework of Orlicz Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating Orlicz first order variation of the width integrals, and call as Orlicz mixed width integrals. The fundamental notions and conclusions of the width integrals and Minkoswki and Brunn-Minkowski inequalities for the width integrals are extended to an Orlicz setting and the related concepts and inequalities of Lp mixed width integrals of convex body are also derived.