Orlicz version of the mixed width integrals

TL;DR

This paper extends the concept of width integrals to the Orlicz space, introducing Orlicz mixed width integrals within the Orlicz Brunn-Minkowski framework, and generalizes related inequalities for convex bodies.

Contribution

It introduces Orlicz mixed width integrals and extends classical width integral inequalities to the Orlicz setting, broadening the scope of convex geometric analysis.

Findings

Defined Orlicz mixed width integrals.

Extended Minkowski and Brunn-Minkowski inequalities to Orlicz setting.

Derived inequalities for Lp 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.