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 ≡ 0. If, for every f ∈ F, f and f~((k)) share 0, and |f(z)| ≥ 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 |f(z)| ≥ M whenever f~((k))(z) = h(z) cannot be replaced by the condition that |f(z)| ≥ 0 whenever f~((k))(z) = h(z). This improves some results due to Fang and Zalcman [2] etc.
展开▼
机译：令k为正整数，令M为正数，令F为域D中的亚纯函数族，其所有零均具有至少k的多重性，令h为D中的全纯函数，h≡如果对于每个f∈F，f和f〜（（k））共享0，并且| f（z）|为0。当f〜（（k））（z）= h（z）时≥M，则F在D中是正常的。f和f〜（（k））等于0的条件不能弱化，并且| f （z）|当f〜（（k））（z）= h（z）不能由| f（z）|的条件代替时，≥M当f〜（（k））（z）= h（z）时≥0。由于Fang和Zalcman [2]等，这改善了一些结果。
展开▼
