FRACTAL DIMENSION VARIATION OF CONTINUOUS FUNCTIONS UNDER CERTAIN OPERATIONS

Binyan Yu and Yongshun Liang ()
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Binyan Yu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Yongshun Liang: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-16

Abstract: In this paper, we make research on the fractal structure of the space of continuous functions and explore how the fractal dimension of continuous functions under certain operations changes. We prove that any nonzero real power and the logarithm of a positive continuous function can keep the fractal dimensions of bi-Lipschitz invariance closed. For continuous functions having finite zero points, the relationship between its global behavior and the local behavior of its square on zero points has been given. Further, we discuss the fractal dimension of the product of continuous functions and provide the product decomposition of a continuous function in terms of the lower and upper box dimensions. Some special properties of the space of one-dimensional continuous functions have also been shown.

Keywords: Fractal Dimension; Graph of the Function; Continuous Functions (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0218348X23500445

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