Dual Orlicz mixed geominimal surface area

Volume 11, Issue 10, pp 1113--1123 http://dx.doi.org/10.22436/jnsa.011.10.01

Publication Date: June 27, 2018 Submission Date: September 07, 2016 Revision Date: December 13, 2017 Accteptance Date: April 14, 2018

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Authors

Li Gao - College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, P. R. China. Tongyi Ma - College of Mathematics and Statistics, Hexi University, Zhangye, Gansu, 734000, P. R. China. Yuanyuan Guo - College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu, 730070, P. R. China.

Abstract

Based on the classical ideas, Zhu discussed the properties and useful theories for \(L_{p}\)-mixed geominimal surface area; meanwhile, Ma defined dual Orlicz geominimal surface area. The previous studies provide a thought to us for the study of the dual Orlicz mixed geominimal surface. In our paper, we have done the following work: attempting to use an integral form to define the dual Orlicz mixed geominimal surface area, further studyding its related properties, and listing some inequalities including Alexandrov-Fenchel type inequality, analogous cyclic inequality, Blaschke-Santaló type inequality, and affine isoperimetric inequality in Orlicz space.

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Keywords

• Star bodies
• dual Orlicz mixed geominimal surface area
• inequality

MSC

•  52A20
•  52A40

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