Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 26249, 17 pages
New Inequalities on Fractal Analysis and Their Applications
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.
Two new fractal measures and
are constructed from Minkowski contents
and . The properties of these two new measures are
studied. We show that the fractal dimensions Dim and
can be derived from and
, respectively. Moreover, some inequalities about
the dimension of product sets and product measures are obtained.