On Univalence, Multivalence and Infinite-Valence

We investigate whether the conditions sufficient for a function that is analytic and locally univalent to be univalent in the unit disk Ucan be weakened by allowing the above three expressions to lie in a larger domain of variability. It turns out that in various cases the function f can then be inf...

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Bibliographic Details
Published in:Complex variables, theory & application theory & application, 1997-08, Vol.33 (1-4), p.63-74
Main Author: Brannan, David A.
Format: Article
Language:English
Subjects:
finitely valent
infinitely valent
Univalent
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Summary:We investigate whether the conditions sufficient for a function that is analytic and locally univalent to be univalent in the unit disk Ucan be weakened by allowing the above three expressions to lie in a larger domain of variability. It turns out that in various cases the function f can then be infinitely valent in U.
ISSN:0278-1077
1563-5066
DOI:10.1080/17476939708815012