## Abstract

We study the normality of families of meromorphic functions defined in terms of certain omitted functions. In particular, we prove the following results. Firstly, if F is a family of meromorphic functions in a domain D , and a(z), b(z) and c(z) are distinct meromorphic functions in D and if, for all f F and all z D, f(z) a(z), f(z) b(z) and f(z) c(z), then F is normal in D. Secondly, letting R(w) be a rational function of degree greater than or equal to 3 and F be a family of functions meromorphic in a domain D , if there exists a non-constant meromorphic function (z) in D such that, for all f F and z D, R(f(z)) (z), then F is normal in D.

Original language | English |
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Pages (from-to) | 57-72 |

Number of pages | 16 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 139 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2009 |

### Bibliographical note

Funding Information:The research of J.M.C. was supported by the NNSF of China (Grant nos 10871094 and 10671093), by the NSF of Jiangsu, China (Grant no. 08KJB110001) and by the Fred and Barbara Kort Sino-Israel Post Doctoral Fellowship Program at Bar-Ilan University. The research of M.L.F. was supported by the NNSF of China (Grant no. 10771076), the NSF of Guangdong Province, China (Grant no. 07006700) and the Gelbart Research Institute for the Mathematical Sciences at Bar-Ilan University. The research of all three authors was supported by the German-Israeli Foundation for Scientific Research and Development, GIF Grant no. G-809-234-6/2003.

### Funding

The research of J.M.C. was supported by the NNSF of China (Grant nos 10871094 and 10671093), by the NSF of Jiangsu, China (Grant no. 08KJB110001) and by the Fred and Barbara Kort Sino-Israel Post Doctoral Fellowship Program at Bar-Ilan University. The research of M.L.F. was supported by the NNSF of China (Grant no. 10771076), the NSF of Guangdong Province, China (Grant no. 07006700) and the Gelbart Research Institute for the Mathematical Sciences at Bar-Ilan University. The research of all three authors was supported by the German-Israeli Foundation for Scientific Research and Development, GIF Grant no. G-809-234-6/2003.

Funders | Funder number |
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Fred and Barbara Kort Sino–Israel Post Doctoral Fellowship Program at Bar-Ilan University | 10771076 |

Gelbart Research Institute for the Mathematical Sciences at Bar-Ilan University | |

NSF of Guangdong Province | 07006700 |

NSF of Jiangsu | 08KJB110001 |

German-Israeli Foundation for Scientific Research and Development | G-809-234-6/2003 |

National Natural Science Foundation of China | 10671093, 10871094 |