Differential inequalities and a marty-type criterion for Quasi-normality

Jürgen Grahl, Tomer Manket, Shahar Nevo

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We show that the family of all holomorphic functions in a f domain D satisfying |f(k)|/1+|f| (z) ≤ C for all z ∞ D (where k is a natural number and C> 0) is quasi-normal. Furthermore, we give a general counterexample to show that for α> 1 and k≥2 the condition |f(k)|/1+|f|α (z) ≤ C for all z ∞ D does not imply quasi-normality.

Original languageEnglish
Pages (from-to)34-45
Number of pages12
JournalJournal of the Australian Mathematical Society
Issue number1
StatePublished - 1 Aug 2018

Bibliographical note

Publisher Copyright:
© 2018 Australian Mathematical Publishing Association Inc.


  • Marty's theorem
  • differential inequalities
  • normal families
  • quasi-normal families


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