Normality of meromorphic functions whose derivatives have 1-points |
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Authors: | Jianming Chang |
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Affiliation: | 1. Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, People’s Republic of China
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Abstract: | Let k be a positive integer and let ${mathcal F}Let k be a positive integer and let F{mathcal F} be a family of functions meromorphic in a plane domain D, all of whose zeros have multiplicity at least k + 3. If there exists a subset E of D which has no accumulation points in D such that for each function f ? F{finmathcal F}, f (k)(z) − 1 has no zeros in DE{Dsetminus E}, then F{mathcal F} is normal. The number k + 3 is sharp. The proof uses complex dynamics. |
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