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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Binyan Yu & Yongshun Liang, 2022. "Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions," Mathematics, MDPI, vol. 10(13), pages 1-29, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2154-:d:843715
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    Cited by:

    1. Yu, Binyan & Liang, Yongshun, 2024. "On two special classes of fractal surfaces with certain Hausdorff and Box dimensions," Applied Mathematics and Computation, Elsevier, vol. 468(C).

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