A counterexample of a normality criterion for families of meromorphic functions

作者：Fang, Caiyun^*; Xu, Yan

来源：Comptes Rendus Mathematique, 2018, 356(1): 56-62.

DOI：10.1016/j.crma.2017.11.008

Let A > 1 be a constant, and let F be a family of meromorphic functions in a domain D. If, for every function f is an element of F, f has only zeros of multiplicity at least 2 and satisfies the following conditions: (1) f(z) = 0 double right arrow vertical bar f ''(z)vertical bar <= A vertical bar z vertical bar, (2) f ''(z) not equal z, (3) all poles of f have multiplicity at least 4, then F is normal in D. In this paper, we first give an example to show that condition (3) is sharp, and prove that our counterexample is unique in some sense.

• 出版日期2018-1
• 单位南京师范大学