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  • Research Article
  • Open Access

New Inequalities on Fractal Analysis and Their Applications

Journal of Inequalities and Applications20072007:026249

https://doi.org/10.1155/2007/26249

  • Received: 26 September 2006
  • Accepted: 23 November 2006
  • Published:

Abstract

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.

Keywords

  • Fractal Dimension
  • Fractal Analysis
  • Product Measure
  • Fractal Measure
  • Minkowski Content

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Authors’ Affiliations

(1)
Department of Mathematics, Georgetown University, Washington, DC 20057, USA
(2)
School of Computer science and Engineering, South China University of Technology, Guangzhou, 510640, China

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