Applications of Fixed Point Theorems in the Theory of Generalized IFS
By A. Mihail, Radu Miculescu. 2008
81 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b9bbc449c432adb1c19b22c6f7b5e371d1bf69a5
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Existence of the Attractor of Countable Iterated Function Systems (2012, background): “Some interesting results concerning extensions of metric spaces on which the IFSs are defined or the respective contractions can be found, as example, in [3], [13], [20], [17], [23], [25], [10], [14], [18].”