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Research Article | Open Access

Best proximity point results of iterated function systems for α- ψ-contractions

Mustafa Aslantas1( ), Ali Hussein Bachay1,2, Hakan Sahin3, A. Duran Türkoğlu4
Department of Mathematics, Faculty of Science, Çankırı Karatekin University, 18100 Çankırı, Turkey
Department of Business Administration, College of Administration and Economics, University of Sumer, Iraq
Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University, 16310 Bursa, Turkey
Department of Mathematics, Faculty of Science, Gazi University, 06010 Ankara, Turkey
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Abstract

In this paper, we present two new concepts, called α- ψ -iterated function system and α- ψ-proximal iterated function system, by using α- ψ-contractions and α- ψ -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.

Keywords

iterated function systemsfractalsbest proximity point
CLC number: 28A80, 54H25, 47H10

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 19106-19125
DOI: 10.3934/math.2025854

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Cite this article:
Aslantas M, Bachay AH, Sahin H, et al. Best proximity point results of iterated function systems for α- ψ-contractions. AIMS Mathematics, 2025, 10(8): 19106-19125. https://doi.org/10.3934/math.2025854

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Received: 30 December 2024
Revised: 04 August 2025
Accepted: 08 August 2025
Published: 15 August 2025
©2025 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)