Let F be a meromorphic function family on domain D, nN.The conjecture of Hayman says: If each function f(z) of family F satisfies fn(z)f '(z)≠1,then F is normal in D.In the paper we generalize it by allowing f n(z)f '(z) -1 to have zeros, but restricting the values f(z) can take at the zeros of f n(z)f '(z)-1.%设F是区域D上的亚纯函数族,nN.Hayman猜想的正规定则是:如果族F中的每个f(z)都满足f n(z)f '(z)≠1,那么F在D上正规.文章的主要结果推广了它,允许f n(z)f '(z)-1取零值,但在这些零值点处的f(z)值有所限制.
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