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Graphs of continuous functions and fractal dimensions

Author

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  • Verma, Manuj
  • Priyadarshi, Amit

Abstract

In this paper, we show that, for any β∈[1,2], a given strictly positive (or strictly negative) real-valued continuous function on [0,1] whose graph has the upper box dimension less than or equal to β can be decomposed as a product of two real-valued continuous functions on [0,1] whose graphs have upper box dimensions equal to β. We also obtain a formula for the upper box dimension of every element of a ring of polynomials in a finite number of continuous functions on [0,1] over the field R.

Suggested Citation

  • Verma, Manuj & Priyadarshi, Amit, 2023. "Graphs of continuous functions and fractal dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004149
    DOI: 10.1016/j.chaos.2023.113513
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    References listed on IDEAS

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    1. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Megha Pandey & Vishal Agrawal & Tanmoy Som, 2022. "Fractal Dimension Of Multivariate α-Fractal Functions And Approximation Aspects," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-17, November.
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    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).
    3. 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).

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