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Normality of meromorphic functions whose derivatives have 1-points

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Abstract

Let k be a positive integer and let \({\mathcal F}\) 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 \({f\in\mathcal F}\), f (k)(z) − 1 has no zeros in \({D\setminus E}\), then \({\mathcal F}\) is normal. The number k + 3 is sharp. The proof uses complex dynamics.

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Authors and Affiliations

  1. Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu, 215500, People’s Republic of China

    Jianming Chang

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  1. Jianming Chang
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Correspondence to Jianming Chang.

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Research supported by NNSF of China (Grant No. 10871094), NSFU of Jiangsu, China (Grant No. 08KJB110001), Qinglan Project of Jiangsu, China, and SRF for ROCS, SEMf.

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Chang, J. Normality of meromorphic functions whose derivatives have 1-points. Arch. Math. 94, 555–564 (2010). https://doi.org/10.1007/s00013-010-0125-1

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