Abstract
We show that the family Fk of all meromorphic functions f in a domain D satisfying (Formula presented.) (where k is a natural number and C > 0) is quasi-normal. The proof relies mainly on the Zalcman–Pang rescaling lemma which we employ to get estimates for the behaviour of certain quotients of higher derivatives of the functions in Fk at certain points close to a point of non-normality.
Original language | English |
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Pages (from-to) | 73-84 |
Number of pages | 12 |
Journal | Bulletin of the London Mathematical Society |
Volume | 50 |
Issue number | 1 |
DOIs | |
State | Published - 1 Feb 2018 |
Bibliographical note
Publisher Copyright:© 2017 London Mathematical Society
Keywords
- 30A10 (primary)
- 30D45