FRACTAL DIMENSIONS OF LINEAR COMBINATION OF CONTINUOUS FUNCTIONS WITH THE SAME BOX DIMENSION

被引：15
|
作者：
Wang, Xuefei [1 ]
Zhao, Chunxia [1 ]
机构：
[1] Nanjing Univ Sci & Technol, Inst Comp, Nanjing 210094, Peoples R China
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2020年 / 28卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Box Dimension; Variation Linear Combination;
D O I：
10.1142/S0218348X2050139X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we mainly discuss continuous functions with certain fractal dimensions on [0, 1]. We find space of continuous functions with certain Box dimension is not closed. Furthermore, Box dimension of linear combination of two continuous functions with the same Box dimension maybe does not exist. Definitions of fractal functions and local fractal functions have been given. Linear combination of a fractal function and a local fractal function with the same Box dimension must still be the original Box dimension with nontrivial coefficients.
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页数：5
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