• Corpus ID: 238583599

# Applications of the Tarski-Kantorovitch Fixed-Point Principle to the study of Infinite Iterated Function Systems

@inproceedings{Luchian2021ApplicationsOT,
title={Applications of the Tarski-Kantorovitch Fixed-Point Principle to the study of Infinite Iterated Function Systems},
author={Bogdan-Alexandru Luchian},
year={2021}
}
The aim of this paper is to establish some results regarding Infinite Iterated Function Systems with the help of the Tarski-Kantorovitch fixed-point principles for maps on partially ordered sets. To this end we introduce two new classes of Infinite Iterated Function Systems which are well suited for applying the aforementioned principle. We also study some properties of the canonical projection from the shift space of an Infinite Iterated Function System belonging to one of the two introduced…

## References

SHOWING 1-10 OF 10 REFERENCES
The Tarski–Kantorovitch prinicple and the theory of iterated function systems
• Mathematics
Bulletin of the Australian Mathematical Society
• 2000
We show how some results of the theory of iterated function systems can be derived from the Tarski–Kantorovitch fixed–point principle for maps on partialy ordered sets. In particular, this principle
SOME CONSEQUENCES OF THE TARSKI-KANTOROVITCH ORDERING THEOREM IN METRIC FIXED POINT THEORY
Abstract We show that the Tarski-Kantorovitch Principle for continuous maps on a partially ordered set yields some fixed point theorems for contractive maps on a uniform space. Our proofs do not
The contraction principle as a particular case of Kleene's fixed point theorem
It is proved that Kleene's fixed point theorem may be regarded as a particular case of the partially ordered sets and ordered set theorem by embedding a metric space in an ordered set.
THE SHIFT SPACE FOR AN INFINITE ITERATED FUNCTION SYSTEM
• Mathematics
• 2009
The aim of the paper is to define the shift space for an infinite iterated function systems (IIFS) and to describe the relation between this space and the attractor of the IIFS. We construct a
Remetrization results for possibly infinite self-similar systems
• Mathematics
• 2016
In this paper we introduce a concept of possibly infinite self-similar system which generalizes the attractor of a possibly infinite ite\-ra\-ted function system whose constitutive functions are
Some connections between the attractors of an IIFS S and the attractors of the sub-IFSs of S
• Mathematics
• 2012
Based on the results from (Mihail and Miculescu in Math. Rep., Bucur. 11(61)(1):21-32, 2009), where the shift space for an infinite iterated function system (IIFS for short) is defined and the
The canonical projection associated with certain possibly infinite generalized iterated function systems as a fixed point
• Mathematics
Journal of Fixed Point Theory and Applications
• 2018
In this paper, influenced by the ideas from Mihail (Fixed Point Theory Appl 2015:15, 2015), we associate to every generalized iterated function system $$\mathcal {F}$$F (of order m) an operator
Some connections between the attractors of an IIFS S and the attractors of the sub-IFSs of S, Fixed Point Theory Appl
• 2012
Lipscomb ’ s space ω A is the attractor of an infinite IFS containing affine transformations of l 2 p A q
• Proc . Amer . Math . Soc .
• 2008
Mȃsurȃ s , i fractali
• Lucian Blaga
• 2002