IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i13p2154-d843715.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/13/2154/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/13/2154/
    Download Restriction: no
    ---><---

    Citations

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


    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).
    2. 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).

    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:gam:jmathe:v:10:y:2022:i:13:p:2154-:d:843715. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.