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 S be an iterated function system (IFS) with the attractor G_∆, where ∆ is a given data set. We consider an affine transformation ω(∆) of ∆, and we define the IFS Ŝ with the attractor G_ω(∆). We give a sufficient condition so that G_ω(∆) = ω(G_∆). 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.