Generalized iterated function systems on the space l∞(X)

In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-02, Vol.410 (2), p.847-858
Main Author: Secelean, Nicolae-Adrian
Format: Article
Language:English
Subjects:
Attractor
Generalized contractions
Generalized countable iterated function system
Hausdorff–Pompeiu metric
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Summary:In the last decades there has been a current effort to extend the classical Hutchinson theory of iterated function systems composed by contractions on a metric space X into itself to more general spaces and infinitely many mappings. In this paper we consider the (countable) iterated function systems consisting of some generalized contractions on the product space XI into X, where I is an arbitrary set of natural numbers. Some approximations of the attractors of the respective iterated function systems are given.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2013.09.007