@article{Attia2024, 
author = {Najmeddine Attia and Neji Saidi and Rim Amami and Rimah Amami},
title = {On the stability of Fractal interpolation functions with variable parameters},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {2},
pages = {2908-2924},
keywords = {iterated function system (IFS), generalized affine fractal interpolation function, hölder and Lipschitz functions},
url = {https://www.sciopen.com/article/10.3934/math.2024143},
doi = {10.3934/math.2024143},
abstract = {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    ,      α    n    (  x  )  y  +      ψ    n    (  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        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.}
}