Phi-contractive parent-child infinite IFSs and orbital phi-contractive infinite IFSs

Mihail, Alexandru; Savu, Irina

doi:10.48550/arxiv.2103.07551

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E Orbital Iterated Function Systems1

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2022

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“…As for the case of IFSs, one can associate to an orbital iterated function system S its fractal operator. It turns out (see [9] and [11]) that the fractal operator associated to an orbital function system is a weakly Picard operator with respect to the Hausdorff-Pompeiu metric, every of its fixed points being called an attractor of the system.…”

Section: E Orbital Iterated Function Systemsmentioning

confidence: 99%

A characterization of the fuzzy fractals generated by an orbital fuzzy iterated function system

Miculescu¹,

Mihail²,

Savu³

2022

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Orbital fuzzy iterated function systems are obtained as a combination of the concepts of iterated fuzzy set system and orbital iterated function system. It turns out that, for such a system, the corresponding fuzzy operator is weakly Picard, its fixed points being called fuzzy fractals. In this paper we present a structure result concerning fuzzy fractals associated to an orbital fuzzy iterated function system by proving that such an object is perfectly determined by the action of the initial term of the Picard iteration sequence on the closure of the orbits of certain elements.

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Section: E Orbital Iterated Function Systemsmentioning

confidence: 99%