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On the stability of Fractal interpolation functions with variable parameters
- Source :
- AIMS Mathematics, Vol 9, Iss 2, Pp 2908-2924 (2024)
- Publication Year :
- 2024
- Publisher :
- AIMS Press, 2024.
-
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) = \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.
Details
- Language :
- English
- ISSN :
- 24736988
- Volume :
- 9
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- AIMS Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.491156bc2b9b4d86bdc4899ab70aaaa8
- Document Type :
- article
- Full Text :
- https://doi.org/10.3934/math.2024143?viewType=HTML