IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i05ns0218348x23500445.html
   My bibliography  Save this article

Fractal Dimension Variation Of Continuous Functions Under Certain Operations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Binyan Yu & Yongshun Liang, 2023. "Fractal Dimension Variation Of Continuous Functions Under Certain Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500445
    DOI: 10.1142/S0218348X23500445
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X23500445
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X23500445?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gupta, Deepika & Pandey, Asheesh, 2024. "Analyzing impact of corporate governance index on working capital management through fractal functions," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. 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).
    3. Yu, Binyan & Liang, Yongshun, 2024. "On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    4. 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).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:31:y:2023:i:05:n:s0218348x23500445. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.