Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points
Year: 2015
Author: Shaoyuan Xu, Wangbin Xu, Zuoling Zhou
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 92–100
Abstract
In this paper, some results on the upper convex densities of self-similar sets at the contracting-similarity fixed points are discussed. Firstly, a characterization of the upper convex densities of self-similar sets at the contracting-similarity fixed points is given. Next, under the strong separation open set condition, the existence of the best shape for the upper convex densities of self-similar sets at the contracting-similarity fixed points is proven. As consequences, an open problem and a conjecture, which were posed by Zhou and Xu, are answered.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n1.8
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 1 : pp. 92–100
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Self-similar set upper convex density Hausdorff measure and Hausdorff dimension contracting-similarity fixed point.
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