Orlicz mean dual affine quermassintegrals
type: Item
instance of: scholarly article
title: Orlicz mean dual affine quermassintegrals
zbMATH Open document ID: 1387.52019
DOI: 10.1155/2018/8123924
author: Changjian Zhao
author: Wing-Sum Cheung
published in: Journal of Function Spaces
publication date: 2018-04-06T00:00:00Z
review text: Summary: Our main aim is to generalize the mean dual affine quermassintegrals to the Orlicz space. Under the framework of dual Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first Orlicz variation of the mean dual affine quermassintegrals and call it the Orlicz mean dual affine quermassintegral. The fundamental notions and conclusions of the mean dual affine quermassintegrals and the Minkowski and Brunn-Minkowski inequalities for them are extended to an Orlicz setting. The related concepts and inequalities of dual Orlicz mixed volumes are also included in our conclusions. The new Orlicz isoperimetric inequalities in special case yield the \(L_p\)-dual Minkowski inequality and Brunn-Minkowski inequality for the mean dual affine quermassintegrals, which also imply the dual Orlicz-Minkowski inequality and dual Orlicz-Brunn-Minkowski inequality.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 6856698
zbMATH Keywords: Orlicz mean dual affine quermassintegral
zbMATH Keywords: dual Orlicz mixed volumes
zbMATH Keywords: Orlicz isoperimetric inequalities
zbMATH Keywords: dual Orlicz-Minkowski inequality
zbMATH Keywords: dual Orlicz-Brunn-Minkowski inequality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8123924
OpenAlex ID: W2786628714
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description: scientific article; zbMATH DE number 6856698