On the approximation of a convex body by its radial mean bodies
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Authors
Lvzhou Zheng
- School of Mathematics and Statistics, Hubei Normal University, 435002 Huangshi, P. R. China.
Abstract
In this paper, we consider the approximation problem on the volume of a convex body \(K\) in \(\mathbb{R}^n\) by those
of its radial mean bodies \(R_pK\): Specifically, we establish the identity
\[\lim_{p\rightarrow \infty}\frac{P}{\log P}(1-2^{-n}\frac{|R_P(K)|}{|K|})=\frac{n(n+1)}{2};\]
when K is an ellipsoid in \(\mathbb{R}^n\).
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ISRP Style
Lvzhou Zheng, On the approximation of a convex body by its radial mean bodies, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2846--2856
AMA Style
Zheng Lvzhou, On the approximation of a convex body by its radial mean bodies. J. Nonlinear Sci. Appl. (2016); 9(5):2846--2856
Chicago/Turabian Style
Zheng, Lvzhou. "On the approximation of a convex body by its radial mean bodies." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2846--2856
Keywords
- Convex body
- radial mean body
- difference body
- restricted chord projection function.
MSC
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