tailieunhanh - Báo cáo hóa học: "Research Article Some Inequalities for the Lp -Curvature Image"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some Inequalities for the Lp -Curvature Image | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 320786 12 pages doi 2009 320786 Research Article Some Inequalities for the Lp-Curvature Image Wang Weidong 1 2 Wei Daijun 2 and Xiang Yu2 1 Department of Mathematics China Three Gorges University Daxue Road 8 Hubei Yichang 443002 China 2 Department of Mathematics Hubei Institute for Nationalities Hubei Enshi 445000 China Correspondence should be addressed to Wang Weidong wdwxh722@ Received 16 May 2009 Revised 19 August 2009 Accepted 14 October 2009 Recommended by Peter Pang 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. 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. 1. Introduction Let Kn denote the set of convex bodies compact convex subsets with nonempty interiors in Euclidean space Rn for the set of convex bodies containing the origin in their interiors and the set of origin-symmetric convex bodies in Rn we respectively write Kn and K . Let Sn-1 denote the unit sphere in Rn and denote by V K the n-dimensional volume of body K for the standard unit ball B in Rn and denote a. V B . The groups of nonsingular linear transformations and the group of special linear transformations are denoted by GL n and SL n respectively. Suppose that R is the set of real numbers. If K e Kn then its support function hK h K Rn R is defined by see 1 page 16 h K x max x y y e K x e Rn where x y denotes the standard inner product of x .