Generalized Iterated Function Systems on <i>b</i>-Metric Spaces

Abstract

An iterated function system consists of a complete metric space (X,d) and a finite family of contractions f1,⋯,fn:X→X. A generalized iterated function system comprises a finite family of contractions defined on the Cartesian product Xm 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
• <i>b</i>-metric spaces