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Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes
Author
Source
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-16
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
Our main aim is to generalize the classical mixed volume V(K1,…,Kn) and Aleksandrov-Fenchel inequality to the Orlicz space.
In the framework of Orlicz-Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the Orlicz first-order variation of the mixed volume and call it Orlicz multiple mixed volume of convex bodies K1,…,Kn, and Ln, denoted by Vφ(K1,…,Kn,Ln), which involves (n+1) convex bodies in Rn.
The fundamental notions and conclusions of the mixed volume and Aleksandrov-Fenchel inequality are extended to an Orlicz setting.
The related concepts and inequalities of Lp-multiple mixed volume Vp(K1,…,Kn,Ln) are also derived.
The Orlicz-Aleksandrov-Fenchel inequality in special cases yields Lp-Aleksandrov-Fenchel inequality, Orlicz-Minkowski inequality, and Orlicz isoperimetric type inequalities.
As application, a new Orlicz-Brunn-Minkowski inequality for Orlicz harmonic addition is established, which implies Orlicz-Brunn-Minkowski inequalities for the volumes and quermassintegrals.
American Psychological Association (APA)
Zhao, Chang-Jian. 2018. Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes. Journal of Function Spaces،Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1186794
Modern Language Association (MLA)
Zhao, Chang-Jian. Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes. Journal of Function Spaces No. 2018 (2018), pp.1-16.
https://search.emarefa.net/detail/BIM-1186794
American Medical Association (AMA)
Zhao, Chang-Jian. Orlicz-Aleksandrov-Fenchel Inequality for Orlicz Multiple Mixed Volumes. Journal of Function Spaces. 2018. Vol. 2018, no. 2018, pp.1-16.
https://search.emarefa.net/detail/BIM-1186794
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186794