The Characteristic Properties of the Minimal -Mean Width - Download this document for free, or read online. Document in PDF available to download.

Journal of Function Spaces - Volume 2017 2017, Article ID 2943073, 10 pages - https:-doi.org-10.1155-2017-2943073

Research ArticleCollege of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China

Correspondence should be addressed to Tongyi Ma

Received 18 February 2017; Accepted 23 March 2017; Published 20 June 2017

Academic Editor: Antonio S. Granero

Copyright © 2017 Tongyi Ma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Giannopoulos proved that a smooth convex body has minimal mean width position if and only if the measure , supported on , is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal -mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal -mean width of convex bodies and prove the existence and uniqueness of the minimal -mean width in its images. In addition, we establish a characterization of the minimal -mean width, conclude the average with a variation of the minimal -mean width position, and give the condition for the minimum position of .





Author: Tongyi Ma

Source: https://www.hindawi.com/

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