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

Song-Il Ri; Gwang-Jin O; Gyong-Jin Jo; Chol-U Pak; In-Son Ri; Song-Il Ri; Gwang-Jin O; Gyong-Jin Jo; Chol-U Pak; In-Son Ri

doi:10.3934/math.2026549

AIMS Mathematics

2026, Volume 11, Issue 5: 13304-13338. doi: 10.3934/math.2026549

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

1.
Department of Mathematics, University of Science, Pyongyang, DPR Korea
2.
Department of Control Science, University of Science, Pyongyang, DPR Korea
3.
Department of Mathematics, Pyongyang University of Transport, Pyongyang, DPR Korea

Received: 12 December 2025 Revised: 24 February 2026 Accepted: 10 March 2026 Published: 13 May 2026
MSC : 27A80, 37L30

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.
- fixed-point theorem,
- Bryant contraction mapping,
- Rakotch contraction mapping,
- iterated function systems (IFSs),
- fractal interpolation functions (FIFs)
Citation: Song-Il Ri, Gwang-Jin O, Gyong-Jin Jo, Chol-U Pak, In-Son Ri. Key results obtained during the search for contractive mappings that can generate fractal interpolation functions[J]. AIMS Mathematics, 2026, 11(5): 13304-13338. doi: 10.3934/math.2026549

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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.

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