On bivariate fractal interpolation for countable data and associated nonlinear fractal operator

• Autorzy: Pandey Kshitij Kumar , Secelean Nicolae Adrian , Viswanathan Puthan Veedu

Identyfikatory

DOI

10.1515/dema-2024-0014

• Języki publikacji: EN

Abstrakty

EN

Fractal interpolation has been conventionally treated as a method to construct a univariate continuous function interpolating a given finite data set with the distinguishing property that the graph of the interpolating function is the attractor of a suitable iterated function system. On the one hand, attempts have been made to extend the univariate fractal interpolation from a finite data set to a countably infinite set. On the other hand, fractal interpolation in higher dimensions, particularly the theory of fractal interpolation surfaces (FISs), has received increasing attention for more than a quarter century. This article targets a twofold extension of the notion of fractal interpolation by providing a general framework to construct FISs for a prescribed set consisting of countably infinite data on a rectangular grid. By using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function. Some elementary properties of the associated nonlinear (not necessarily linear) fractal operators are established, thereby allowing the interaction of the notion of fractal interpolation with the theory of nonlinear operators.

Słowa kluczowe

EN

bivariate fractal interpolation; countable data set; alpha-fractal function; fractal operator; nonlinear operators; perturbation of operators

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240014
• Opis fizyczny: Bibliogr. 42 poz.

Twórcy

autor

Pandey Kshitij Kumar

• Department of Mathematics, IIT Delhi, New Delhi, 110016, India

autor

Secelean Nicolae Adrian

• Department of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Sibiu, Romania

autor

Viswanathan Puthan Veedu

• Department of Mathematics, IIT Delhi, New Delhi, 110016, India

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).