Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 320786, 12 pages
doi:10.1155/2009/320786
Research Article

Some Inequalities for the Lp-Curvature Image

Wang Weidong,1,2 Wei Daijun,2 and Xiang Yu2

1Department of Mathematics, China Three Gorges University, Daxue Road 8, Hubei Yichang 443002, China
2Department of Mathematics, Hubei Institute for Nationalities, Hubei Enshi 445000, China

Received 16 May 2009; Revised 19 August 2009; Accepted 14 October 2009

Academic Editor: Peter Pang

Copyright © 2009 Wang Weidong et al. 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

Lutwak introduced the notion of Lp-curvature image and proved an inequality for the volumes of convex body and its Lp-curvature image. In this paper, we first give an monotonic property of Lp-curvature image. Further, we establish two inequalities for the Lp-curvature image and its polar, respectively. Finally, an inequality for the volumes of Lp-projection body and Lp-curvature image is obtained.