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arXiv · 2112.11196

Definite Integral of $α$-Fractal Functions

Md Nazimul Islam·Imrul Kaish
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Abstract

In this article the integration of the $α$-fractal interpolation function $f^α$ corresponding to any continuous function $f$ on a compact interval $I$ of $\mathbb{R}$ is estimated although there is no explicit form of $α$-fractal interpolation function till now. Some results related to the definite integral of $f^α$ are established. Also the flipped $α$-fractal function $f_{F}^{α_{F}}$ corresponding to the continuous function $f$ is constructed and a result is proved that relates the definite integrals of the fractal functions $f_{F}^{α_{F}}$ and $f^α$.

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Md Nazimul Islam, Imrul Kaish. 2021-12-20. Definite Integral of $α$-Fractal Functions. https://arxiv.org/abs/2112.11196

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