In this paper we provide another characterization of hyperbolic diameter diminishing to zero iterated function systems that
were studied in [R. Miculescu, A. Mihail, Diameter diminishing to zero IFSs, arXiv:2101.12705]. The primary tool that we use is an operator H_{\mathcal{S}}, associated to the iterated function system \mathcal{S}, which is inspired by the similar one utilized in Mihail (Fixed Point Theory Appl., 2015:75, 2015). Some fixed point results are also obtained as by products of our main result.

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  Păcurar, Cristina-Maria,  Mihail, Alexandru, Miculescu, Radu