In:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), Vol. 134, No. 4 ( 2004-08), p. 653-660
Abstract:
We show that there exists a function f , meromorphic in the plane C, such that the family of all functions g holomorphic in the unit disc D for which f ∘ g has no fixed point in D is not normal. This answers a question of Hinchliffe, who had shown that this family is normal if Ĉ\ f (C) does not consist of exactly one point in D. We also investigate the normality of the family of all holomorphic functions g such that f ( g ( z )) ≠ h ( z ) for some non-constant meromorphic function h .
Type of Medium:
Online Resource
ISSN:
0308-2105
,
1473-7124
DOI:
10.1017/S0308210500003401
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2004
detail.hit.zdb_id:
209230-X
detail.hit.zdb_id:
2036780-6
SSG:
11
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