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On the dimensional connection between a class of real number sequences and local fractal functions with a single unbounded variation point

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  • Yu, Binyan
  • Liang, Yongshun

Abstract

In this paper, we investigate the connection between a class of real number sequences and local fractal functions in terms of fractal dimensions. Under certain conditions, we show that the Box dimension of the graph of a local fractal function with a single unbounded variation point is equal to that of its zero points set plus one. Several concrete examples of such functions whose Box dimension can take any numbers belonging to [1,2] have also been given. This work may provide new approaches to the construction of various local fractal functions with the required Box dimension in the future.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004879
    DOI: 10.1016/j.chaos.2024.114935
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    References listed on IDEAS

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    1. Verma, Manuj & Priyadarshi, Amit, 2023. "Graphs of continuous functions and fractal dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Binyan Yu & Yongshun Liang, 2024. "Construction Of Monotonous Approximation By Fractal Interpolation Functions And Fractal Dimensions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-15.
    3. 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.
    4. Lal, Rattan & Chandra, Subhash & Prajapati, Ajay, 2024. "Fractal surfaces in Lebesgue spaces with respect to fractal measures and associated fractal operators," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Binyan Yu & Yongshun Liang, 2024. "Research On Fractal Dimensions And The Hã–Lder Continuity Of Fractal Functions Under Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-28.
    6. Binyan Yu & Yongshun Liang, 2023. "Fractal Dimension Variation Of Continuous Functions Under Certain Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-16.
    7. Chandra, Subhash & Abbas, Syed, 2022. "Fractal dimensions of mixed Katugampola fractional integral associated with vector valued functions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    8. Y. S. Liang, 2022. "Approximation With Fractal Functions By Fractal Dimension," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-12, November.
    9. Verma, S. & Jha, S. & Navascués, M.A., 2023. "Smoothness analysis and approximation aspects of non-stationary bivariate fractal functions," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    10. Dong Yang & Xia Yuan & Kang Zhang & Shiwei Wu & Chunxia Zhao, 2024. "A One-Dimensional Continuous Function With Unbounded Variation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-6.
    11. Subhash Chandra & Syed Abbas & Yongshun Liang, 2024. "A Note On Fractal Dimension Of Riemann–Liouville Fractional Integral," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-14.
    12. Yong-Shun Liang, 2022. "Approximation Of The Same Box Dimension In Continuous Functions Space," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-9, May.
    13. Xie, T.F. & Zhou, S.P., 2007. "On a class of fractal functions with graph Hausdorff dimension 2," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1625-1630.
    Full references (including those not matched with items on IDEAS)

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