Note on fractal interpolation function with variable parameters

Najmeddine Attia; Taoufik Moulahi; Rim Amami; Neji Saidi

doi:10.3934/math.2024127

Note on fractal interpolation function with variable parameters

Najmeddine Attia, Taoufik Moulahi, Rim Amami, Neji Saidi

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions (Formula Presented). Then, we may define the generalized affine FIF f interpolating a given data set (Formula Presented), where (Formula Presented). In this paper, we discuss the smoothness of the FIF f . We prove, in particular, that f is θ-hölder function whenever ψ_n are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.

Original language	English
Pages (from-to)	2584-2601
Number of pages	18
Journal	AIMS Mathematics
Volume	9
Issue number	2
DOIs	https://doi.org/10.3934/math.2024127
State	Published - 2024

Keywords

generalized affine fractal interpolation function
hölder and Lipschitz functions
iterated function system

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10.3934/math.2024127

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abstract = "Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions (Formula Presented). Then, we may define the generalized affine FIF f interpolating a given data set (Formula Presented), where (Formula Presented). In this paper, we discuss the smoothness of the FIF f . We prove, in particular, that f is θ-h{\"o}lder function whenever ψn are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.",

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author = "Najmeddine Attia and Taoufik Moulahi and Rim Amami and Neji Saidi",

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AU - Attia, Najmeddine

AU - Moulahi, Taoufik

AU - Amami, Rim

AU - Saidi, Neji

PY - 2024

Y1 - 2024

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AB - Fractal interpolation function (FIF) is a new method of constructing new data points within the range of a discrete set of known data points. Consider the iterated functional system defined through the functions (Formula Presented). Then, we may define the generalized affine FIF f interpolating a given data set (Formula Presented), where (Formula Presented). In this paper, we discuss the smoothness of the FIF f . We prove, in particular, that f is θ-hölder function whenever ψn are. Furthermore, we give the appropriate upper bound of the maximum range of FIF in this case.

KW - generalized affine fractal interpolation function

KW - hölder and Lipschitz functions

KW - iterated function system

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JO - AIMS Mathematics

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Note on fractal interpolation function with variable parameters

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