Fractal interpolation over nonlinear partitions

This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition funct...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2022-09, Vol.162, p.112503, Article 112503
Main Author: Massopust, Peter R.
Format: Article
Language:English
Subjects:
Attractor
Fractal function
Fractal interpolation
Iterated function system (IFS)
Lebesgue–Bochner space
Perturbation
Read-Bajraktarević operator
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Summary:This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition functions are considered and sufficient conditions for the existence of a unique solution of the underlying fractal interpolation problem for some classes of function spaces are given. •Introduces the fractal interpolation problem over domains with a nonlinear partition.•Extends known methods and presents a new holistic approach to fractal interpolation.•Perturbations of nonlinear partition functions are considered.•Derives sufficient conditions for unique solutions in Bochner–Lebesgue and Cα spaces.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.112503