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New Inequalities on Fractal Analysis and Their Applications

Journal of Inequalities and Applications volume 2007, Article number: 026249 (2007) Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, Georgetown University, Washington, DC, 20057, USA

    Der-Chen Chang

  2. School of Computer science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Yong Xu

Authors
  1. Der-Chen Chang
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  2. Yong Xu
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Correspondence to Der-Chen Chang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chang, DC., Xu, Y. New Inequalities on Fractal Analysis and Their Applications. J Inequal Appl 2007, 026249 (2007). https://doi.org/10.1155/2007/26249

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

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