Generalized Iterated Function Systems on b -Metric Spaces

Izabella Abraham () and Radu Miculescu
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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

Mathematics, 2023, vol. 11, issue 13, 1-16

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.

Keywords: fractals; iterated function systems; fixed points; attractor; b -metric spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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