科研之友
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摘要
Let k be a positive integer, let M be a positive number, let F be a family of meromorphic functions in a domain D, all of whose zeros are of multiplicity at least k, and let h be a holomorphic function in D, h not equivalent to 0. If, for every f is an element of F, f and f((k)) share 0, and vertical bar f(z)vertical bar >= M whenever f((k))(z) = h(z), then F is normal in D. The condition that f and f((k)) share 0 cannot be weakened, and the condition that vertical bar f(z)vertical bar >= M whenever f((k))(z) = h(z) cannot be replaced by the condition that vertical bar f(z)vertical bar >= 0 whenever f((k))(z) = h(z). This improves some results due to Fang and Zalcman [2] etc.
