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Definite Integral Of α-Fractal Functions

Author

Listed:
  • MD NAZIMUL ISLAM

    (Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, Kolkata 700 160, India)

  • IMRUL KAISH

    (Department of Mathematics and Statistics, Aliah University, IIA/27, New Town, Kolkata 700 160, India)

Abstract

A fractal interpolation function (FIF) is a special type of continuous function defined on a compact interval I of ℠which interpolates a certain data set and whose graph is of fractal nature. But an α-fractal (interpolation) function is a special type of FIF which is a fractal analogue corresponding to any continuous function f defined on the interval I. In this paper, the definite integral of the α-fractal function fα corresponding to any continuous function f on the interval I is estimated although there is no explicit form of α-fractal function till now. Some results related to the definite integral of fα are established. Also, the flipped α-fractal function fFαF corresponding to the continuous function f is constructed and a result is proved that relates the definite integrals of the fractal functions fFαF and fα.

Suggested Citation

  • Md Nazimul Islam & Imrul Kaish, 2022. "Definite Integral Of α-Fractal Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-7, September.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:06:n:s0218348x22501031
    DOI: 10.1142/S0218348X22501031
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