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Definite Integral of \\(\\alpha\\)-Fractal Functions
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Definite Integral of \\(\\alpha\\)-Fractal Functions
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Paper
Definite Integral of \\(\\alpha\\)-Fractal Functions
2021
Overview
In this article the integration of the \\(\\alpha\\)-fractal interpolation function \\(f^{\\alpha}\\) corresponding to any continuous function \\(f\\) on a compact interval \\(I\\) of \\(\\mathbb{R}\\) is estimated although there is no explicit form of \\(\\alpha\\)-fractal interpolation function till now. Some results related to the definite integral of \\(f^{\\alpha}\\) are established. Also the flipped \\(\\alpha\\)-fractal function \\(f_{F}^{\\alpha_{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}^{\\alpha_{F}}\\) and \\(f^{\\alpha}\\).
Publisher
Cornell University Library, arXiv.org
Subject
