On the stability of Fractal interpolation functions with variable parameters

Fractal interpolation function (FIF) is a fixed point of the Read–Bajraktarević operator defined on a suitable function space and is constructed via an iterated function system (IFS). In this paper, we considered the generalized affine FIF generated through the IFS defined by the functions $W_n(x,y)=(a_n(x)+e_n,{\alpha }_n(x)y+{\psi }_n(x))$, $n=1,\dots ,N$. We studied the shift of the fractal interpolation curve, by computing the error estimate in response to a small perturbation on ${\alpha }_n(x)$. In addition, we gave a sufficient condition on the perturbed IFS so that it satisfies the continuity condition. As an application, we computed an upper bound of the maximum range of the perturbed FIF.