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Fractal Dimension Of Product Of Continuous Functions With Box Dimension

Author

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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)

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.

Suggested Citation

  • Peizhi Liu & Yumeng Du & Yongshun Liang, 2023. "Fractal Dimension Of Product Of Continuous Functions With Box Dimension," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-8.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:03:n:s0218348x23500214
    DOI: 10.1142/S0218348X23500214
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    Cited by:

    1. Verma, Manuj & Priyadarshi, Amit, 2024. "A note on the dimensions of difference and distance sets for graphs of functions," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).

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