关于某些连续函数线性组合的分形维数估计
A Remark on the Fractal Dimensions Estimation of the Linear Combination of Continuous Functions
DOI: 10.12677/PM.2022.124060, PDF,  被引量    国家自然科学基金支持
作者: 刘沛智, 杜雨萌, 叶子秦, 梁永顺：南京理工大学，数学与统计学院，江苏 南京
关键词: 分形函数；Box维数；线性组合；Fractal Function； Box Dimension； Linear Combination
摘要: 本文主要研究了某类分形函数线性组合的分形维数。讨论了具有不同上、下Box维数分形函数线性组合的上、下Box维数估计，得到如下结果。一些情形下，线性组合函数具有与原函数相关的上Box维数或下Box维数。而其他情形下，线性组合函数的上、下Box维数数值均是不确定的。
Abstract: In the present paper, we mainly investigate the fractal dimensions of the linear combination of certain fractal functions. We discuss the estimation of Upper and Lower Box dimension of the linear combination of fractal functions having different Upper and Lower Box dimension, and have obtained the following results. In some cases, the linear combination function has Upper or Lower Box dimension that is related to the original function. In other cases, Upper and Lower Box dimen-sion of the linear combination function is uncertain.
文章引用：刘沛智, 杜雨萌, 叶子秦, 梁永顺. 关于某些连续函数线性组合的分形维数估计[J]. 理论数学, 2022, 12(4): 540-548. https://doi.org/10.12677/PM.2022.124060

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