BOUNDED VARIATION ON THE SIERPIŃSKI GASKET

S. Verma and A. Sahu ()
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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

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-12

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.

Keywords: Sierpinski Gasket; Box Dimension; Hausdorff Dimension; Bounded Variation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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DOI: 10.1142/S0218348X2250147X

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