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|Title:||Uniformly bounded components of normality||Authors:||Wang, X.
|Issue Date:||Jul-2007||Citation:||Wang, X., Zhou, W. (2007-07). Uniformly bounded components of normality. Mathematical Proceedings of the Cambridge Philosophical Society 143 (1) : 85-101. ScholarBank@NUS Repository. https://doi.org/10.1017/S0305004107000060||Abstract:||Suppose that f(z) is a transcendental entire function and that the Fatou set F(f) ‡ ∅. Set B1(f):=supU sup z∈U log(|z| + 3)/infw∈U log(|w| + 3) and B 2(f):=supU supz∈U log(|z| + 30)/inf w∈U log(|w| + 3), where the supremum supU is taken over all components of F(f). If B1(f) < ∞ or B 2(f) < ∞, then we say F(f) is strongly uniformly bounded or uniformly bounded respectively. We show that, under some conditions, F(f) is (strongly) uniformly bounded. © 2007 Cambridge Philosophical Society.||Source Title:||Mathematical Proceedings of the Cambridge Philosophical Society||URI:||http://scholarbank.nus.edu.sg/handle/10635/105452||ISSN:||03050041||DOI:||10.1017/S0305004107000060|
|Appears in Collections:||Staff Publications|
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