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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
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