FRACTAL DIMENSION OF PRODUCT OF CONTINUOUS FUNCTIONS WITH BOX DIMENSION

Peizhi Liu, Yumeng Du and Yongshun Liang
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Peizhi Liu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China
Yumeng Du: 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 03, 1-8

Abstract: This paper investigates fractal dimension of product of continuous functions with Box dimension on [0, 1]. For two continuous functions with different Box dimensions, the Box dimension of their product has been proved to be the larger one. Furthermore, the Box dimension of product of two continuous functions with the same Box dimension may not exist. Definitions of regular fractal and local fractal functions have been given. Product of a regular fractal function and a local fractal function with the same Box dimension must still be the original Box dimension.

Keywords: Fractal Functions; Fractal Dimension; Product of Continuous Functions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500214

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