TY - JOUR
T1 - Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points
AU - Shaoyuan Xu , 
AU - Wangbin Xu , 
AU - Zuoling Zhou , 
JO - Analysis in Theory and Applications
VL - 1
SP - 92
EP - 100
PY - 2017
DA - 2017/01
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n1.8
UR - https://global-sci.org/intro/article_detail/ata/4625.html
KW - Self-similar set, upper convex density, Hausdorff measure and Hausdorff dimension, contracting-similarity fixed point.
AB - <p style="text-align: justify;">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.</p>