DEFINITE INTEGRAL OF α-FRACTAL FUNCTIONS

Md Nazimul Islam and Imrul Kaish
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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

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-7

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.

Keywords: α-Fractal Function; Definite Integral of α-Fractal Function; Flipped α-Fractal Function (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501031

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