Normality relationships between two function families and their applications

Let \(\mathcal {F}\) be a family of meromorphic functions in a domain D, and \(\mathcal {F}_k\) be a family of kth derivative functions of all \(f\in \mathcal {F}\). In this paper, we study normality relationships between \(\mathcal {F}\) and \(\mathcal {F}_k\), and obtain some normality criteria. Some applications of our results are given.