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On normal criterion of meromorphic functions. (English) Zbl 0706.30024
This paper is a continuation of work of the author in [Sci. China, Ser. A 32, No.7, 782-791 (1989; Zbl 0687.30023)] which makes use of L. Zalcman’s heuristic principle for normality: a family of holomorphic functions which have a common property P in a domain D is (apt to be) a normal family in D if P cannot be possessed by a non-constant entire function in the finite plane. The author uses a modified version of Zalcman’s principle to establish the normality of the family of meromorphic functions $f\left(z\right)$ satisfying ${f}^{\text{'}}-a{f}^{n}\ne b$, $n\ge 4$, $a\ne 0$, $\infty$, $b\ne \infty$ in a domain D. This conjecture of W. K. Hayman [Research problems in function theory (1967; Zbl 0158.063)] was proved for $n\ge 5$ by L. Xianjin [Sci. Sin. Ser. A 28 (1985)].
Reviewer: St.Dragosh

##### MSC:
 30D45 Bloch functions, normal functions, normal families
##### Keywords:
Bloch’s principle; normal family