Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 26249, 17 pages
doi:10.1155/2007/26249
Research Article

New Inequalities on Fractal Analysis and Their Applications

Der-Chen Chang1 and Yong Xu2

 1Department of Mathematics, Georgetown University, Washington 20057, DC, USA
2School of Computer science and Engineering, South China University of Technology, Guangzhou 510640, China
Received 26 September 2006; Revised 22 November 2006; Accepted 23 November 2006

Recommended by Wing-Sum Cheung

Abstract

Two new fractal measures M*s and M*s are constructed from Minkowski contents M*s and M*s. The properties of these two new measures are studied. We show that the fractal dimensions Dim and δ^ can be derived from M*s and M*s, respectively. Moreover, some inequalities about the dimension of product sets and product measures are obtained.