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Research Article | Open Access

Key results obtained during the search for contractive mappings that can generate fractal interpolation functions

Song-Il Ri1, Gwang-Jin O1( ), Gyong-Jin Jo1, Chol-U Pak2, In-Son Ri3
Department of Mathematics, University of Science, Pyongyang, DPR Korea
Department of Control Science, University of Science, Pyongyang, DPR Korea
Department of Mathematics, Pyongyang University of Transport, Pyongyang, DPR Korea
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Abstract

In this paper, we show that, through two counterexamples, iterated function systems consisting of Bryant contraction mappings cannot generate fractals in general. Also, we present two new families of Rakotch contraction mappings that can generate new fractal interpolation functions with a wide range of applications in practice.

Keywords

fixed-point theoremBryant contraction mappingRakotch contraction mappingiterated function systems (IFSs)fractal interpolation functions (FIFs)
CLC number: 27A80, 37L30

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AIMS Mathematics
Volume 11 Issue 5,
May 2026
Pages 13304-13338
DOI: 10.3934/math.2026549

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Cite this article:
Ri S-I, O G-J, Jo G-J, et al. Key results obtained during the search for contractive mappings that can generate fractal interpolation functions. AIMS Mathematics, 2026, 11(5): 13304-13338. https://doi.org/10.3934/math.2026549

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Received: 12 December 2025
Revised: 24 February 2026
Accepted: 10 March 2026
Published: 15 May 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)