IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i07ns0218348x2250147x.html
   My bibliography  Save this article

Bounded Variation On The Sierpiåƒski Gasket

Author

Listed:
  • S. VERMA

    (Department of Applied Sciences, IIIT Allahabad, Prayagraj 211015, Uttar Pradesh, India)

  • A. SAHU

    (��School of Advanced Sciences and Languages, VIT Bhopal University, Bhopal 466114, Madhya Pradesh, India)

Abstract

Under certain continuity conditions, we estimate upper and lower box dimensions of the graph of a function defined on the Sierpiński gasket. We also give an upper bound for Hausdorff dimension and box dimension of the graph of a function having finite energy. Further, we introduce two sets of definitions of bounded variation for a function defined on the Sierpiński gasket. We show that fractal dimension of the graph of a continuous function of bounded variation is log 3 log 2. We also prove that the class of all bounded variation functions is closed under arithmetic operations. Furthermore, we show that every function of bounded variation is continuous almost everywhere in the sense of log 3 log 2-dimensional Hausdorff measure.

Suggested Citation

  • S. Verma & A. Sahu, 2022. "Bounded Variation On The Sierpiåƒski Gasket," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-12, November.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x2250147x
    DOI: 10.1142/S0218348X2250147X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X2250147X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X2250147X?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. Verma, Shubham Kumar & Kumar, Satish, 2024. "Fractal dimension analysis of financial performance of resulting companies after mergers and acquisitions," Chaos, Solitons & Fractals, Elsevier, vol. 181(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:30:y:2022:i:07:n:s0218348x2250147x. 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.