Proof of Hayman’s conjecture on normal families. (English) Zbl 0592.30035

Li, Xian-Jin

Sci. Sin., Ser. A 28, 596-603 (1985).

The author presents a proof for one of the conjectures which appeared in the work of W. K. Hayman [Research problems in function theory. London: University of London. The Athlone Press (1967; Zbl 0158.06301)]. If \({\mathcal F}\) is a family of meromorphic functions \(f\) in a domain \(D\) satisfying \(f'(z)-af(z)^ n\neq b\), where \(n\geq 5\) and a and b are fixed finite constants, then \({\mathcal F}\) is a normal family in \(D\).

Reviewer: St.Dragosh

MSC:

30D45	Normal functions of one complex variable, normal families
30D30	Meromorphic functions of one complex variable (general theory)
30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory

Keywords:

normal family

Citations:

Zbl 0158.06301