# Stability of multivalued attractors

## TL;DR

This paper demonstrates that attractors of continuous multivalued maps are stable and can be derived using a Banach theorem variant, extending classical results to multivalued dynamics in metric spaces.

## Contribution

It introduces a Banach converse theorem variant for multivalued maps and establishes stability of their attractors in metric spaces.

## Key findings

- Attractors of continuous multivalued maps are stable.
- Such attractors can be obtained via the Banach theorem in hyperspaces.
- The results extend classical stability theorems to multivalued dynamics.

## Abstract

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 in a metric space are stable. Moreover, such attractors in locally compact, complete metric spaces may be obtained by means of the Banach theorem in the hyperspace.