Normal families of meromorphic functions concerning differential polynomials (Q2839887)

In this paper the authors give an example showing that the third condition in a theorem on normal families of meromorphic functions due to \textit{X. Huang} and \textit{Y. Gu} [Result. Math. 49, No. 3--4, 279--288 (2006; Zbl 1126.30022)] is sharp. Furthermore, they prove an important theorem which shows that their counterexample is unique in some sense. Then the result of Huang and Gu [loc. cit.] is derived from two normality criteria obtained in this paper.