Premium
Normal families and omitted functions II
Author(s) -
Zhang Guoming,
Pang Xuecheng,
Zalcman Lawrence
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn103
Subject(s) - mathematics
Let k ⩾ 2 be an integer and let ℱ be a family of functions meromorphic on a domain D in ℂ, all of whose poles are multiple and whose zeros all have multiplicity at least k + 1. Let h be a function meromorphic on D , h ≢ 0, ∞. Suppose that for each f ∈ ℱ, f ( k ) ( z ) ≠ h ( z ) for z ∈ D . Then ℱ is a normal family on D .