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