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Approximation With Fractal Functions By Fractal Dimension

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  • Y. S. LIANG

    (School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China)

Abstract

On the basis of previous studies, we explore the approximation of continuous functions with fractal structure. We first give the calculation of fractal dimension of the linear combination of continuous functions with different Hausdorff dimension. Fractal dimension estimation of the linear combination of continuous functions with the same Hausdorff dimension has also been discussed elementary. Then, based on Weierstrass Theorem and the related results of Weierstrass function, we give the conclusion that the linear combination of polynomials with the same Hausdorff dimension approximates the objective function. The corresponding results with noninteger and integer Hausdorff dimensions have been investigated. We also give the preliminary applications of the theory in the last section.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:07:n:s0218348x22501511
    DOI: 10.1142/S0218348X22501511
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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).
    2. Agathiyan, A. & Gowrisankar, A. & Fataf, Nur Aisyah Abdul, 2024. "On the integral transform of fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 209-224.

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