A new approach to fractals via best proximity point

Ishak Altun, Hakan Sahin and Mustafa Aslantas

Chaos, Solitons & Fractals, 2021, vol. 146, issue C

Abstract: In this paper, we present a new approach to fractals through best proximity points, inspired by the remarkable relationship between fixed point theory and fractal theory. In this way, we introduce the concept of proximal IFS generated by a finite set of proximal contractions to expand the concept of IFS, one of the most common methods of creating fractals. Thus, as a new method of obtaining fractal we present a result showing that the proximal IFS has a unique best attractor under the certain conditions on metric spaces. To support our new result an illustrative example is given.

Keywords: Fractals; Best proximity point; Iterated function systems; Fixed point (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002034

DOI: 10.1016/j.chaos.2021.110850

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