ORLICZ MULTIPLE AFFINE QUERMASSINTEGRALS

Chang-Jian Zhao

doi:10.11948/20190154

2021 Volume 11 Issue 2

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Chang-Jian Zhao. ORLICZ MULTIPLE AFFINE QUERMASSINTEGRALS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 632-655. doi: 10.11948/20190154

Citation:

Chang-Jian Zhao. ORLICZ MULTIPLE AFFINE QUERMASSINTEGRALS[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 632-655. doi: 10.11948/20190154

ORLICZ MULTIPLE AFFINE QUERMASSINTEGRALS

Chang-Jian Zhao^,

Department of Mathematics, China Jiliang University, Hangzhou 310018, China

Corresponding author: Email: chjzhao@163.com(C. Zhao)
Fund Project: The author was supported by National Natural Science Foundation of China(10971205, 11371334)

Abstract

Abstract

In the paper, our main aim is to generalize the mixed affine quermassintegrals of j convex bodies to the Orlicz space. We find a new affine geometric quantity by calculating first-order variation and call it Orlicz multiple affine quermassintegrals. The mixed affine quermassintegrals and AleksandrovFenchel inequality for the mixed affine quermassintegrals of j convex bodies are extended to an Orlicz setting. A new Orlicz-Aleksandrov-Fenchel inequality for the mixed affine quermassintegrals of j convex bodies is established. The new Orlicz-Aleksandrov-Fenchel inequality in special cases yield the classical Aleksandrov-Fenchel inequality for mixed volumes, the Aleksandrov-Fenchel inequality for the mixed affine quermassintegrals which is just built, and Zou's Orlicz Minkowski inequality for affine quermassintegrals, respectively. This new concept of L_p-multiple affine quermassintegrals and L_p-AleksandrovFenchel inequality for the L_p-multiple affine quermassintegrals is also derived. Moreover, the Orlicz multiple mixed volumes and the Orlicz-AleksandrovFenchel inequality for the mixed volumes are also included in our new conclusions. As an application, a new Orlicz-Brunn-Minkowski inequality for the mixed affine quermassintegrals of j convex bodies is proved.
- Affine quermassintegral /
- L_p-addition /
- Orlicz addition /
- Orlicz affine quermassintegral /
- Orlicz multiple mixed volume /
- Orlicz-Aleksandrov-Fenchel inequality for the mixed volume
MSC: 46E30, 52A39, 52A40

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References

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