On the stability of Fractal interpolation functions with variable parameters

• Published in: AIMS mathematics Vol. 9; no. 2; pp. 2908 - 2924
• Main Authors: Attia, Najmeddine, Saidi, Neji, Amami, Rim, Amami, Rimah
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: generalized affine fractal interpolation function; hölder and lipschitz functions; iterated function system (ifs)
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2024143

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, \alpha_n(x) y +\psi_n(x)\big) $, $ n = 1, \ldots, 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.