On linear transformation of generalized affine fractal interpolation function

In this work, we investigate a class of generalized affine fractal interpolation functions (FIF) with variable parameters, where ordinate scaling is substituted by a real-valued control function. Let $\mathcal{S}$ be an iterated function system (IFS) with the attractor $G_{\mathrm{\Delta }}$, where $\mathrm{\Delta }$ is a given data set. We consider an affine transformation $\omega (\mathrm{\Delta })$ of $\mathrm{\Delta }$, and we define the IFS $\hat{\mathcal{S}}$ with the attractor $G_{\omega (\mathrm{\Delta })}$. We give a sufficient condition so that $G_{\omega (\mathrm{\Delta })}=\omega (G_{\mathrm{\Delta }})$. In addition, we compare the definite integrals of the corresponding FIF and study the additivity property. Some examples will be given, highlighting the effectiveness of our results.