On the Fractal interpolation functions associated with Matkowski contractions

In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function $ f $, we study a new class of fractal interpolation functions which converge to $ f $