Remarkable results obtained when studying a question concerning the invariant set of an IFS

Song-Il Ri, Vasileios Drakopoulos, Gyong-Jin Jo and Yong-Sop U

Chaos, Solitons & Fractals, 2024, vol. 187, issue C

Abstract: Some years ago, a question was raised about whether an iterated function system consisting of a finite number of Reich (or Kannan) contractions (generally discontinuous contractive mappings) has a unique compact invariant set. In this article, we give remarkable results obtained by studying previous research articles that tried to answer this question positively and previous counterexamples that demonstrate that this question is negatively answered. Our results strongly encourage the development of fractal theory because the existence, uniqueness, compactness and boundedness of invariant sets with respect to functional families are one of the main research topics in the theory of fractals.

Keywords: Banach contraction principle; Kannan fixed point theorem; Iterated function system (IFS); Fractals; Attractor (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924009500

DOI: 10.1016/j.chaos.2024.115398

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