Definite Integral of $\alpha$-Fractal Functions

Abstract

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 $f^{\alpha }$.