A note on normality of meromorphic functions

Let F be a family of all functions f meromorphic in a domain D C C, for which, all zeros have multiplicity at least k, and f(Z) = 0 double left right arrow f((k))(Z) = 1 double right arrow vertical bar f((k+1))(Z)vertical bar <= h, where k is an element of N and h is an element of R+ are given. Examples show that T is not normal in general (at least for k = 1 or k = 2). The example we give for k = 1 shows that a recent result of Y. Xu [5] is not correct. However, we prove that for k not equal 2, there exists a positive integer K is an element of N such that the subfamily 9 = {f is an element of F : all possible poles of f in D have multiplicity at least K} of T is normal. This generalizes our result in [1]. The case k = 2 is also considered.