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On a class of fractal functions with graph Hausdorff dimension 2

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  • Xie, T.F.
  • Zhou, S.P.

Abstract

We prove that the graph of the continuous functiony=Φ(x)=∑k=1∞λ-kαϕλkβx,0⩽x⩽1has Hausdorff dimension 2, where λ>1, β>α>1, ϕ(x)=2x, 0⩽x⩽1/2, ϕ(−x)=ϕ(x) and ϕ(x+1)=ϕ(x).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:5:p:1625-1630
    DOI: 10.1016/j.chaos.2005.12.038
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    References listed on IDEAS

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    1. He, G.L. & Zhou, S.P., 2005. "What is the exact condition for fractional integrals and derivatives of Besicovitch functions to have exact box dimension?," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 867-879.
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    Cited by:

    1. 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).

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