Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions

Binyan Yu and Yongshun Liang
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Binyan Yu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China
Yongshun Liang: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, China

Mathematics, 2022, vol. 10, issue 13, 1-29

Abstract: In the present paper, we try to estimate the fractal dimensions of the linear combination of continuous functions with different fractal dimensions. Initially, a general method to calculate the lower and the upper Box dimension of the sum of two continuous functions by classifying all the subsequences into different sets has been proposed. Further, we discuss the majority of possible cases of the sum of two continuous functions with different fractal dimensions and obtain their corresponding fractal dimensions estimation by using that general method. We prove that the linear combination of continuous functions having no Box dimension cannot keep the fractal dimensions closed. In this way, we have figured out how the fractal dimensions of the linear combination of continuous functions change with certain fractal dimensions.

Keywords: the fractal dimension; the linear combination; continuous functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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