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A Normality Criterion Corresponding to the Defect Relations

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Abstract

Let \(\mathcal{{F}}\) be a family of meromorphic functions on a domain D. We present a quite general sufficient condition for \(\mathcal{{F}}\) to be a normal family. This criterion contains many known results as special cases. The overall idea is that certain comparatively weak conditions on \(\mathcal{{F}}\) by local arguments lead to somewhat stronger conditions, which in turn lead to even stronger conditions on the limit function g in the famous Zalcman Lemma. Ultimately, the defect relations for g force normality of \(\mathcal{{F}}\).

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Correspondence to Andreas Schweizer.

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Communicated by Lawrence Zalcman.

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Schweizer, A. A Normality Criterion Corresponding to the Defect Relations. Comput. Methods Funct. Theory 17, 591–601 (2017). https://doi.org/10.1007/s40315-017-0196-0

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  • DOI: https://doi.org/10.1007/s40315-017-0196-0

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