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

Academic Editor: Wing-Sum Cheung

Copyright © 2007 Der-Chen Chang and Yong Xu. 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

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.