Best proximity point results of iterated function systems for $ \alpha $-$ \psi $-contractions

Mustafa Aslantas; Ali Hussein Bachay; Hakan Sahin; A. Duran Türkoğlu; Mustafa Aslantas; Ali Hussein Bachay; Hakan Sahin; A. Duran Türkoğlu

doi:10.3934/math.2025854

AIMS Mathematics

2025, Volume 10, Issue 8: 19106-19125. doi: 10.3934/math.2025854

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Research article

Best proximity point results of iterated function systems for $ \alpha $-$ \psi $-contractions

1.
Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18100 Çankırı, Turkey
2.
Department of Business Administration, College of Administration and Economics, University of Sumer, Iraq
3.
Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, 16310 Bursa, Turkey
4.
Department of Mathematics, Faculty of Science, Gazi University, 06010 Ankara, Turkey

Received: 30 December 2024 Revised: 04 August 2025 Accepted: 08 August 2025 Published: 22 August 2025
MSC : 28A80, 54H25, 47H10

In this paper, we present two new concepts, called $ \alpha $-$ \psi $ -iterated function system and $ \alpha $-$ \psi $-proximal iterated function system, by using $ \alpha $-$ \psi $-contractions and $ \alpha $-$ \psi $ -proximal contractions. Hence, we extended and generalized some definitions existing in the literature. We present some results that determine the necessary conditions to obtain a fractal with an attractor in the mentioned systems. Finally, some interesting examples are presented to apply our results.
- iterated function systems,
- fractals,
- best proximity point
Citation: Mustafa Aslantas, Ali Hussein Bachay, Hakan Sahin, A. Duran Türkoğlu. Best proximity point results of iterated function systems for $ \alpha $-$ \psi $-contractions[J]. AIMS Mathematics, 2025, 10(8): 19106-19125. doi: 10.3934/math.2025854

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Abstract

In this paper, we present two new concepts, called $ \alpha $-$ \psi $ -iterated function system and $ \alpha $-$ \psi $-proximal iterated function system, by using $ \alpha $-$ \psi $-contractions and $ \alpha $-$ \psi $ -proximal contractions. Hence, we extended and generalized some definitions existing in the literature. We present some results that determine the necessary conditions to obtain a fractal with an attractor in the mentioned systems. Finally, some interesting examples are presented to apply our results.

References

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