On the graphs of products of continuous functions and fractal dimensions

Liu, Jia; Shi, Saisai; Zhang, Yuan

doi:10.1007/s10473-023-0610-9

Acta Math Sci

2023

DOI: 10.1007/s10473-023-0610-9

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On the graphs of products of continuous functions and fractal dimensions

Jia Liu,

Saisai Shi,

Yuan Zhang

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Cited by 3 publications

References 14 publications

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A note on the dimensions of difference and distance sets for graphs of functions

Verma,

Priyadarshi

2024

Chaos, Solitons & Fractals

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A note on the dimensions of difference and distance sets for graphs of functions

Verma,

Priyadarshi

2024

Chaos, Solitons & Fractals

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General multifractal dimensions of measures

Selmi

2025

Fuzzy Sets and Systems

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Research on Fractal Dimensions and the Hölder Continuity of Fractal Functions Under Operations

YU,

LIANG

2024

Fractals

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Based on the previous studies, we make further research on how fractal dimensions of graphs of fractal continuous functions under operations change and obtain a series of new results in this paper. Initially, it has been proven that a positive continuous function under unary operations of any nonzero real power and the logarithm taking any positive real number that is not equal to one as the base number can keep the fractal dimension invariable. Then, a general method to calculate the Box dimension of two continuous functions under binary operations has been proposed. Using this method, the lower and upper Box dimensions of the product and the quotient of continuous functions without zero points have been investigated. On this basis, these conclusions will be generalized to the ring of rational functions. Furthermore, we discuss the Hölder continuity of continuous functions under operations and then prove that a Lipschitz function can be absorbed by any other continuous functions under certain binary operations in the sense of fractal dimensions. Some elementary results for vector-valued continuous functions have also been given.

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On the graphs of products of continuous functions and fractal dimensions

Cited by 3 publications

References 14 publications

A note on the dimensions of difference and distance sets for graphs of functions

A note on the dimensions of difference and distance sets for graphs of functions

General multifractal dimensions of measures

Research on Fractal Dimensions and the Hölder Continuity of Fractal Functions Under Operations

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