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- Title
The Generalized L<sub>p</sub>-mixed Volume and the Generalized L<sub>p</sub>-mixed Projection Body.
- Authors
Tongyi Ma
- Abstract
In this paper, based on three classical concept of the mixed surface area measure, the mixed volumes and the mixed projection bodies, we introduce three new concepts of the generalized Lp-mixed surface area measure, the generalized Lp- mixed volumes and the generalized Lp-mixed projection bodies of convex bodies. In addition, some important inequalities, such as, the Aleksandrov-Fenchel inequality for the generalized Lp-mixed volumes, the Aleksandrov-Fenchel inequality for the generalized Lp-mixed projection bodies and the Brunn-Minkowski inequality for polar of Lp-mixed projection bodies are established, respectively. We also give a generalization of Pythagorean inequality and Loomis-Whitney inequality for Lp- mixed volumes, respectively.
- Subjects
CONVEX bodies; PYTHAGOREAN theorem; SURFACE area
- Publication
IAENG International Journal of Applied Mathematics, 2019, Vol 49, Issue 3, p262
- ISSN
1992-9978
- Publication type
Article