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Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors

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  • Yun, CholHui
  • Ri, MiGyong

Abstract

We estimate the bounds for box-counting dimension of hidden variable fractal interpolation functions (HVFIFs) and hidden variable bivariate fractal interpolation functions (HVBFIFs) with four function contractivity factors and present analytic properties of HVFIFs which are constructed to ensure more flexibility and diversity in modeling natural phenomena. Firstly, we construct the HVFIFs and analyze their smoothness and stability. Secondly, we obtain the lower and upper bounds for box-counting dimension of the HVFIFs. Finally, in the similar way, we get the lower and upper bounds for box-counting dimension of HVBFIFs in [Yun CH and Li MK, Hidden variable bivariate fractal interpolation functions and errors on perturbations of function vertical scaling factors, AEJM, 2019; 12(2), doi:10.1142/s 1793557119500219].

Suggested Citation

  • Yun, CholHui & Ri, MiGyong, 2020. "Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301028
    DOI: 10.1016/j.chaos.2020.109700
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    References listed on IDEAS

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    1. Yun, Chol-hui & O, Hyong-chol & Choi, Hui-chol, 2014. "Construction of fractal surfaces by recurrent fractal interpolation curves," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 136-143.
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    Cited by:

    1. Ri, SongIl, 2021. "A remarkable fact for the box dimensions of fractal interpolation curves of R3," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Yao, Kui & Chen, Haotian & Peng, W.L. & Wang, Zekun & Yao, Jia & Wu, Yipeng, 2021. "A new method on Box dimension of Weyl-Marchaud fractional derivative of Weierstrass function," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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    1. Ri, SongIl, 2021. "A remarkable fact for the box dimensions of fractal interpolation curves of R3," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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