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
in a domain D. This conjecture of W. K. Hayman
[Research problems in function theory (1967; Zbl 0158.063
)] was proved for
by L. Xianjin
[Sci. Sin. Ser. A 28 (1985)].