On the Fractal interpolation functions associated with Matkowski contractions

Najmeddine Attia; Mohamed balegh; Rim Amami; Rimah Amami

doi:10.3934/ERA.2023238

On the Fractal interpolation functions associated with Matkowski contractions

Najmeddine Attia^*
, Mohamed balegh
, Rim Amami
, Rimah Amami

^*Corresponding author for this work

King Faisal University
King Khalid University

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

8 Scopus citations

Abstract

In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function f, we study a new class of fractal interpolation functions which converge to f.

Original language	English
Pages (from-to)	4652-4668
Number of pages	17
Journal	Electronic Research Archive
Volume	31
Issue number	8
DOIs	https://doi.org/10.3934/ERA.2023238
State	Published - 2023

Keywords

Banach contraction
fractal interpolation function
generalized iterated function system
iterated function system
Matkowski contraction

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10.3934/ERA.2023238

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abstract = "In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function f, we study a new class of fractal interpolation functions which converge to f.",

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author = "Najmeddine Attia and Mohamed balegh and Rim Amami and Rimah Amami",

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AU - Attia, Najmeddine

AU - balegh, Mohamed

AU - Amami, Rim

AU - Amami, Rimah

N1 - Publisher Copyright: © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

PY - 2023

Y1 - 2023

N2 - In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function f, we study a new class of fractal interpolation functions which converge to f.

AB - In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function f, we study a new class of fractal interpolation functions which converge to f.

KW - Banach contraction

KW - fractal interpolation function

KW - generalized iterated function system

KW - iterated function system

KW - Matkowski contraction

UR - https://www.scopus.com/pages/publications/85167921428

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DO - 10.3934/ERA.2023238

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VL - 31

SP - 4652

EP - 4668

JO - Electronic Research Archive

JF - Electronic Research Archive

IS - 8

ER -

On the Fractal interpolation functions associated with Matkowski contractions

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