Some Results on the Upper Convex Densities of the Self-Similar Sets at the Contracting-Similarity Fixed Points  

作　　者：Shaoyuan Xu Wangbin Xu Zuoling Zhou 

机构地区：[1]School of Maths and Statistics, Hanshan Normal University [2]School of Maths and Statistics, Hubei Normal University [3]School of Lingnan, Zhongshan University

出　　处：《Analysis in Theory and Applications》2015年第1期92-100,共9页分析理论与应用（英文刊）

基　　金：partially supported by the foundation of the research item of Strong Department of Engineering Innovation, which is sponsored by the Strong School of Engineering Innovation of Hanshan Normal University, China, 2013;partially supported by National Natural Science Foundation of China (No. 11371379)

摘　　要：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.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.

关 键 词：Self-similar set upper convex density Hausdorff measure and Hausdorff dimension contracting-similarity fixed point. 

分 类 号：O177.91[理学—数学]