Quasinormality of order 1 for families of meromorphic functions
Both normality and quasinormality of meromorphic functions were introduced by Montel. However, the quasinormality is not as far-reaching as the normality. The authors continued their study of quasinormality of meromorphic functions on a domain in this paper. They proved that for a given integer \(k\geq 1\) and a domain \(D\subset\mathbb{C}\), a quasinormal family \(\mathcal F\) of meromorphic functions on \(D\), all of whose zeros have multiplicity \(\geq k+1\), is quasinormal of order one, if \(f^{(k)}(z)\not=1\) for each \(f\in\mathcal F\) and \(z\in D\).
scientific article; zbMATH DE number 2149312