Journal of Function Spaces
Volume 2017, Article ID 2943073, 10 pages
https://doi.org/10.1155/2017/2943073
The Characteristic Properties of the Minimal -Mean Width
College of Mathematics and Statistics, Hexi University, Zhangye, Gansu 734000, China
Correspondence should be addressed to Tongyi Ma; moc.621@iygnotam
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 .