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Research Article | Open Access

On the Fractal interpolation functions associated with Matkowski contractions

Najmeddine Attia1( ), Mohamed balegh2, Rim Amami3, Rimah Amami4
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, Abha 61413, Saudi Arabia
Department of Basic Sciences, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, Dammam 34212, Saudi Arabia
Computer Department, Deanship of Preparatory Year and Supporting Studies, Imam Abdulrahman Bin Faisal University, Dammam 34212, Saudi Arabia
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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.

Keywords

fractal interpolation functioniterated function systemgeneralized iterated function systemMatkowski contractionBanach contraction

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Electronic Research Archive
Volume 31 Issue 8,
August 2023
Pages 4652-4668
DOI: 10.3934/era.2023238

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Cite this article:
Attia N, balegh M, Amami R, et al. On the Fractal interpolation functions associated with Matkowski contractions. Electronic Research Archive, 2023, 31(8): 4652-4668. https://doi.org/10.3934/era.2023238

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Received: 04 April 2023
Revised: 01 June 2023
Accepted: 15 June 2023
Published: 15 August 2023
©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)