TY - JOUR
T1 - On the stability of Fractal interpolation functions with variable parameters
AU - Attia, Najmeddine
AU - Saidi, Neji
AU - Amami, Rim
AU - Amami, Rimah
N1 - Publisher Copyright:
© 2024 the Author(s), licensee AIMS Press.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - generalized affine fractal interpolation function
KW - hölder and Lipschitz functions
KW - iterated function system (IFS)
UR - https://www.scopus.com/pages/publications/85183623528
U2 - 10.3934/math.2024143
DO - 10.3934/math.2024143
M3 - Article
AN - SCOPUS:85183623528
SN - 2473-6988
VL - 9
SP - 2908
EP - 2924
JO - AIMS Mathematics
JF - AIMS Mathematics
IS - 2
ER -