On normal families and a result of Drasin. (English) Zbl 0556.30025

Let n be an integer not less than 5, and let a and b be complex numbers with \(a\neq 0\). Let f be a family of functions meromorphic in a domain D such that for each f in F, \(f'(z)-af^ n(z)=b\) has no solutions in D. Then F is a normal family in D. Some lemmas of Gu Yongxing (Y. Ku) [Sci. Sin. 21, 431-445 (1978)] are used in the proof. D. Drasin [Acta Math. 122, 231-263 (1969; Zbl 0176.028)] proved the analogous theorem for analytic functions in D.
Reviewer: L.R.Sons


30D45 Normal functions of one complex variable, normal families


Zbl 0176.028
Full Text: DOI


[1] Yang, Sci.Sinica 14 pp 1262– (1965)
[2] Sci. Sinica 21 pp 431– (1978)
[3] DOI: 10.1007/BF02392012 · Zbl 0176.02802
[4] Hayman, Meromorphic Functions (1964)
[5] DOI: 10.2307/1969890 · Zbl 0088.28505
[6] Hayman, Research Problems in Function Theory (1967) · Zbl 0158.06301
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.