We obtain Edelstein-Suzuki type theorems for multivalued mappings in compact b-metric spaces. Moreover, we prove the
existence of coincidence and common fixed points of a hybrid pair of mappings that satisfies Edelstein-Suzuki type contractive
condition. We present some examples along with a comparison with results in existing literature. In the end, we present some
corollaries in the metric spaces with applications in best approximation theory.