Stimulated by recent problems in the theory of iterated function systems, we provide a variant of the Banach converse theorem for multivalued maps. In particular, we show that attractors of continuous multivalued maps on metric spaces are stable. Moreover, such attractors in locally compact, complete metric spaces may be obtained by means of the Banach theorem in the hyperspace.
"Stability of multivalued attractor." Topol. Methods Nonlinear Anal. 53 (1) 97 - 109, 2019. https://doi.org/10.12775/TMNA.2019.002