Some results on value distribution of meromorphic functions. (English) Zbl 1085.30030

Zhang, Wen-Hua

Bull. Malays. Math. Sci. Soc. (2) 28, No. 1, 47-53 (2005).

Several theorems on normality criteria for meromorphic functions and families of meromorphic functions are proved using value distribution theory. As an example on obtained results the following theorem is stated: Let \(\mathcal F\) be a family of meromorphic functions on the unit disc \(\Delta\). Let \(a\) be a finite non-zero complex number and let \(k\) be a positive integer. If for every function \(f\in\mathcal F\), \(f\) has no zeros and \(ff^{(k)}\neq a\), then \(\mathcal F\) is normal on \(\Delta\).

Reviewer: Rauno Aulaskari (Joensuu)

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D45	Normal functions of one complex variable, normal families

Keywords:

meromorphic functions; normal family