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

Access to Document

10.3934/math.2024127

Cite this

@article{c32cb21d11564f84a04417def80432fe,

title = "Note on fractal interpolation function with variable parameters",

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.",

keywords = "generalized affine fractal interpolation function, h{\"o}lder and Lipschitz functions, iterated function system",

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

note = "Publisher Copyright: {\textcopyright} 2024 the Author(s), licensee AIMS Press.",

year = "2024",

doi = "10.3934/math.2024127",

language = "English",

volume = "9",

pages = "2584--2601",

journal = "AIMS Mathematics",

issn = "2473-6988",

publisher = "American Institute of Mathematical Sciences",

number = "2",

}

TY - JOUR

T1 - Note on fractal interpolation function with variable parameters

AU - Attia, Najmeddine

AU - Moulahi, Taoufik

AU - Amami, Rim

AU - Saidi, Neji

PY - 2024

Y1 - 2024

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85180721066

U2 - 10.3934/math.2024127

DO - 10.3934/math.2024127

M3 - Article

AN - SCOPUS:85180721066

SN - 2473-6988

VL - 9

SP - 2584

EP - 2601

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 2

ER -

Note on fractal interpolation function with variable parameters

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this