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Smoothness analysis and approximation aspects of non-stationary bivariate fractal functions

Author

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  • Verma, S.
  • Jha, S.
  • Navascués, M.A.

Abstract

The present note aims to establish the notion of non-stationary bivariate α-fractal functions and discusses some of their approximation properties. We see that using a sequence of iterated function systems generalizes the existing stationary fractal interpolation function (FIF). Also, we show the existence of Borel probability fractal measures supported on the graph of the non-stationary fractal function. Further, we define a fractal operator associated with the constructed non-stationary FIFs, and many applications of this operator such as fractal approximation and the existence of fractal Schauder bases are observed. In the end, we study the constrained approximation with the proposed interpolant.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009049
    DOI: 10.1016/j.chaos.2023.114003
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    References listed on IDEAS

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    1. Peter Massopust, 2019. "Non-Stationary Fractal Interpolation," Mathematics, MDPI, vol. 7(8), pages 1-14, July.
    2. Subhash Chandra & Syed Abbas, 2021. "The Calculus Of Bivariate Fractal Interpolation Surfaces," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-13, May.
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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. Saâdaoui, Foued, 2024. "Segmented multifractal detrended fluctuation analysis for assessing inefficiency in North African stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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