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Generalized Iterated Function Systems on b -Metric Spaces

Author

Listed:
  • Izabella Abraham

    (Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50, 500091 Braşov, Romania)

  • Radu Miculescu

    (Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50, 500091 Braşov, Romania)

Abstract

An iterated function system consists of a complete metric space ( X , d ) and a finite family of contractions f 1 , ⋯ , f n : X → X . A generalized iterated function system comprises a finite family of contractions defined on the Cartesian product X m with values in X . In this paper, we want to investigate generalized iterated function systems in the more general setting of b -metric spaces. We prove that such a system admits a unique attractor and, under some further restrictions on the b -metric, it depends continuously on parameters. We also provide two examples of generalized iterated function systems defined on a particular b -metric space and find the corresponding attractors.

Suggested Citation

  • Izabella Abraham & Radu Miculescu, 2023. "Generalized Iterated Function Systems on b -Metric Spaces," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2826-:d:1177885
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