On linear transformation of generalized affine fractal interpolation function

Abstract

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_\Delta $, where $ \Delta $ is a given data set. We consider an affine transformation $ \omega(\Delta) $ of $ \Delta $, and we define the IFS $ \hat {\mathcal S} $ with the attractor $ G_{\omega(\Delta)} $. We give a sufficient condition so that $ G_{\omega(\Delta)} = \omega(G_\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.

Keywords

• iterated function system
• generalized affine fractal interpolation function
• linear transformation