NORMAL FAMILIES OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS

Huang and Gu[10] proved that a family F of meromorphic functions in a domain D is normal, if, for two analytic functions a(z)(not equivalent to 0), b(z) in D and all f is an element of F, (1) f (z) not equal infinity when a(z) = 0;(2) f'(z) - a(z)f(2)(z) not equal b(z); (3) all poles of f(z) are of multiplicity at least 4. 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. Also, two normality criteria are given, which extend the result of Huang and Gu.