A new multivalued contraction and stability of its fixed point sets

In this paper we obtain some stability results for fixed point sets associated with a sequence of multivalued mappings. We define multivalued α–ψα–ψ contractions and multivalued αα-admissible mappings. We use Hausdorff distance in our definition. We show that the fixed point sets of uniformly convergent sequences of multivalued α–ψα–ψ contractions which are also assumed to be multivalued αα-admissible, are stable under certain conditions. The multivalued mappings we define here are not necessarily continuous. We present two illustrative examples and one open problem.