### Abstract

Let φ: [0, 1) → (0, ∞) be an increasing function. A meromorphic function f in the unit disc is said to be φ -normal if its spherical derivative f^{#}(z):=|f′(z)|/(1 +|f(z)|^{2}) satisfies f^{#}(z) = O{script} (φ(|z|)) as |z| → 1^{-}. This article is devoted to the study of meromorphic φ-normal functions. In particular, an analogue of the Lohwater-Pommerenke theorem and several equivalent characterizations for φ-normal functions are established under certain regularity conditions on φ.

Original language | English |
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Pages (from-to) | 855-863 |

Number of pages | 9 |

Journal | Complex Variables and Elliptic Equations |

Volume | 54 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2009 |

### Keywords

- Bloch function
- Chordal distance
- Meromorphic function
- Normal family
- Normal function
- Spherical derivative
- Unit disc

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

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## Cite this

Aulaskari, R., Makhmutov, S., & Rättyä, J. (2009). Results on meromorphic φ -normal functions.

*Complex Variables and Elliptic Equations*,*54*(9), 855-863. https://doi.org/10.1080/17476930902998860