Stability Properties for Multi-Valued Contractions in Complete Vector-Valued B-Metric Spaces

In this paper, we present some existence and stability results for the fixed point inclusion in the case of multi-valued self contractions, on a complete vector-valued B-metric space. Our main existence result for the fixed point problem extends to the multi-valued setting with a recent result obtained for the single-valued case. Moreover, data dependence on the operator perturbation of the fixed point set and some stability theorems (Ulam–Hyers stability, well-posedness and Ostrowski stability) are proved, in order to have a complete study of the fixed point inclusion.