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Non-Stationary Fractal Functions on the Sierpiński Gasket

Author

Listed:
  • Anuj Kumar

    (Department of Mathematics, Siddharth University Kapilvastu, Siddharthnagar 272202, India
    These authors contributed equally to this work.)

  • Salah Boulaaras

    (Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
    These authors contributed equally to this work.)

  • Shubham Kumar Verma

    (Council of Finance and Mathematical Research, New Delhi 110016, India
    These authors contributed equally to this work.)

  • Mohamed Biomy

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

Following the work on non-stationary fractal interpolation ( Mathematics 7, 666 (2019)), we study non-stationary or statistically self-similar fractal interpolation on the Sierpiński gasket (SG). This article provides an upper bound of box dimension of the proposed interpolants in certain spaces under suitable assumption on the corresponding Iterated Function System. Along the way, we also prove that the proposed non-stationary fractal interpolation functions have finite energy.

Suggested Citation

  • Anuj Kumar & Salah Boulaaras & Shubham Kumar Verma & Mohamed Biomy, 2024. "Non-Stationary Fractal Functions on the Sierpiński Gasket," Mathematics, MDPI, vol. 12(22), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3463-:d:1515323
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    References listed on IDEAS

    as
    1. S. Verma & A. Sahu, 2022. "Bounded Variation On The Sierpiåƒski Gasket," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(07), pages 1-12, November.
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