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Applications of Fixed Point Theorems in the Theory of Generalized IFS

Abstract

We introduce the notion of a generalized iterated function system (GIFS), which is a finite family of functions , where is a metric space and . In case that is a compact metric space and the functions are contractions, using some fixed point theorems for contractions from to , we prove the existence of the attractor of such a GIFS and its continuous dependence in the 's.

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Correspondence to Radu Miculescu.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Mihail, A., Miculescu, R. Applications of Fixed Point Theorems in the Theory of Generalized IFS. Fixed Point Theory Appl 2008, 312876 (2008). https://doi.org/10.1155/2008/312876

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  • DOI: https://doi.org/10.1155/2008/312876

Keywords

  • Point Theorem
  • Differential Geometry
  • Computational Biology
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