Generalized Iterated Function Systems on b-Metric Spaces

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.