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An application of Edelstein’s contraction principle: the attractor of a graph-directed generalized iterated function system

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Abstract

This paper gathers two generalizations of iterated function systems, namely the one introduced by the first two authors under the name of generalized iterated function systems and the one introduced by Mauldin and Williams and Boore and Falconer under the label of graph-directed iterated function systems. By combining them we introduce the concept of a graph-directed generalized iterated function system. We prove that, under suitable contractivity assumptions on the constitutive functions of such a system and structural assumptions on the underlying metric space, it generates, via Edelstein’s contraction principle, a unique attractor. The result is illustrated by two examples.

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Acknowledgements

The authors are very grateful to the reviewers and to the editor whose extremely generous and valuable remarks and comments brought substantial improvements to the paper.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Transilvania University of Braşov, Iuliu Maniu Street, nr. 50, 500091, Braşov, Romania

    Radu Miculescu

  2. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei Street 14, 010014, Bucharest, Romania

    Alexandru Mihail

  3. Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042, Bucharest, Romania

    Silviu-Aurelian Urziceanu

Authors
  1. Radu Miculescu
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  2. Alexandru Mihail
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  3. Silviu-Aurelian Urziceanu
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Correspondence to Radu Miculescu.

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Miculescu, R., Mihail, A. & Urziceanu, SA. An application of Edelstein’s contraction principle: the attractor of a graph-directed generalized iterated function system. J. Fixed Point Theory Appl. 24, 63 (2022). https://doi.org/10.1007/s11784-022-00978-1

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