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 Wₙ(x, y) = (aₙ(x)+eₙ, αₙ(x) y +ψₙ(x)), n = 1, …, N. We studied the shift of the fractal interpolation curve, by computing the error estimate in response to a small perturbation on αₙ(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.