On the stability of Fractal interpolation functions with variable parameters - Attia, Najmeddine; Saidi, Neji; Amami, Rim; Amami, Rimah (AIMS mathematics, 2024)
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) = \big(a_n(x)+e_n, α_n(x) y +ψ_n(x)\big) $, $ n = 1, …, N $. We studied the shift of the fractal interpolation curve, by computing the error estimate in response to a small perturbation on $ α_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.