In our previous work we have shown that if for any initial point there exists a trajectory of a nonexpansive set-valued mapping attracted by a given set, then this property is stable under small perturbations of the mapping. In the present paper we obtain several extensions of this result.
"Convergence to Attractors of Nonexpansive Set-Valued Mappings." Commun. Math. Anal. 22 (1) 51 - 60, 2019.