Journal Article10.1007/S11784-015-0264-X
Reich-type iterated function systems
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TL;DR: In this article, the authors introduce the concept of Reich-type iterated function systems and prove the existence and uniqueness of the attractor of such a system and study the properties of the canonical projection from the code space onto its attractor.
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Abstract: In this paper, we introduce the concept of Reich-type iterated function system and prove the existence and uniqueness of the attractor of such a system. Moreover, we study the properties of the canonical projection from the code space onto the attractor of such a system. We also present an iterated function system consisting of continuous Reich contractions having more than one attractor.
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Citations
Generalized enriched cyclic contractions with application to generalized iterated function system
TL;DR: In this article , a new class of cyclic contraction mappings and a related fixed point theorem in the framework of a Banach space were established. But the convergence of these mappings was not analyzed.
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IFSs consisting of generalized convex contractions
Flavian Georgescu
- 26 Jan 2017
TL;DR: In this article, the authors introduced the concept of iterated function systems consisting of generalized convex contractions and proved that FS is a Picard operator for such a system, where FS is defined by a finite family of continuous functions.
Interpolative operators: Fractal to multivalued fractal
Bellamkonda Prithvi,S. K. Katiyar +1 more
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TL;DR: In this article , an interpolative iterated operator system (I δ -IOS) is employed to approach attractors, particularly fractals; ergo, an iterative operator approach is employed for the first time in the literature.
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Approximating the Attractor Set of Iterated Function Systems of Order m by $$\alpha $$ α -Dense Curves
TL;DR: In this paper, a sequence of finite sets which approximates, with arbitrarily small and controlled error, the attractor set of a (finite or countable) given iterated function system of order m is constructed.
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Answers to questions on ćirić type theorems
TL;DR: In this article, the authors study open questions on Ciric type theorems proposed by Petrusel and construct a counterexample to illustrate obtained results and also to disprove results similar to Theorems 4.1 and 4.2 for a multi-fractal map generated by an iterated multivalued system of multi-valued maps of Ciric types.
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References
Some Remarks Concerning Contraction Mappings
TL;DR: In this paper, the following result was proved: the Lipschitz constant k < 1 for a complete metric space with fixed points u and un respectively is a contraction mappings of X into itself.
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Multivalued fractals in b-metric spaces
TL;DR: In this article, the authors extend the study of fractal operator theory for multivalued operators on complete b-metric spaces to the case of complete or compact metric spaces.
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Iterated function systems consisting of F-contractions
TL;DR: In this article, a particular case of a contractive self-mapping on a complete metric space, namely the F-contraction introduced by Wardowski (fixed point theory Appl. 87, 2012), is considered, and some new properties of it are provided.
On a certain generalisation of the iterated function system
Filip Strobin,Jarosław Swaczyna +1 more
TL;DR: In this paper, the authors follow the idea of generalizing the notion of classical IFSs, which was presented by Mihail and Miculescu, and study the generic aspect of the problem of existence of an attractor of a function system.