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.
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© 2017 London Mathematical Society
- 30A10 (primary)