Relational generalized iterated function systems
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...
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| Vydané v: | Chaos, solitons and fractals Ročník 182; s. 114823 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Ltd
01.05.2024
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| Predmet: | |
| ISSN: | 0960-0779, 1873-2887 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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.
•We introduce the class of relational generalized iterated function systems.•We weaken the classical contraction condition using an equivalence relation.•We prove that each compact set generates an attractor of the system.•We establish a structure result for the attractors.•We prove a theorem concerning the continuous dependence of the attractors. |
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| ISSN: | 0960-0779 1873-2887 |
| DOI: | 10.1016/j.chaos.2024.114823 |