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Relational generalized iterated function systems

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  • Abraham, Izabella
  • Miculescu, Radu
  • Mihail, Alexandru

Abstract

In this paper, we introduce a wider class of generalized iterated function systems, called relational generalized iterated function systems. More precisely, the classical contraction condition for functions defined on product spaces is weakened by means of an equivalence relation. In particular, if we consider the total equivalence relation, we recover the classical generalized iterated function systems. Our main result states that each compact subset of the underlying metric space generates, via a sequence of iterates, a fixed point of the associated fractal operator, called an attractor of the system. We also establish a structure result for the attractors and a theorem concerning the continuous dependence of the attractor on the associated compact set. Ultimately, we provide some examples which illustrate our main results.

Suggested Citation

  • Abraham, Izabella & Miculescu, Radu & Mihail, Alexandru, 2024. "Relational generalized iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003758
    DOI: 10.1016/j.chaos.2024.114823
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    References listed on IDEAS

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    1. Miculescu, Radu & Mihail, Alexandru & Urziceanu, Silviu-Aurelian, 2020. "Contractive affine generalized iterated function systems which are topologically contracting," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Dumitru, Dan & Ioana, Loredana & Sfetcu, Răzvan-Cornel & Strobin, Filip, 2015. "Topological version of generalized (infinite) iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 78-90.
    3. Izabella Abraham & Radu Miculescu, 2023. "Generalized Iterated Function Systems on b -Metric Spaces," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    Full references (including those not matched with items on IDEAS)

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