International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 6, Pages 895-915
doi:10.1155/IJMMS.2005.895
Some new Brunn-Minkowski-type inequalities in convex bodies
Chang-Jian Zhao1
, Gangsong Leng2
and Lokenath Debnath3
1Department of Applied Mathematics, College of Sciences, China Jiliang University, Hangzhou 310014, China
2Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200436, China
3Department of Mathematics, University of Texas - Pan American, Edinburg 78539-2999, TX, USA
Abstract
We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.