Normality and shared sets

Mingling Fang, Lawrence Zalcman

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k+1. Let a and b be distinct finite complex numbers, and let k be a positive integer. If, for each pair of functions f and g in , f(k) and g(k) share the set S={a,b}, then is normal in D. The condition that the zeros of functions in have multiplicity at least k+1 cannot be weakened.

Original languageEnglish
Pages (from-to)339-354
Number of pages16
JournalJournal of the Australian Mathematical Society
Volume86
Issue number3
DOIs
StatePublished - Jun 2009

Bibliographical note

Funding Information:
The research of the first author was supported by the NNSF of China (Grant No. 10771076) and the NSF of Guangdong Province, China. The research of the second author was supported by the German–Israeli Foundation for Scientific Research and Development, Grant G-809-234.6/2003. ©c 2009 Australian Mathematical Society 1446-7887/2009 $16.00

Keywords

  • Meromorphic function
  • Normality
  • Shared set.

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