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Uniformly bounded components of normality

Published online by Cambridge University Press:  01 July 2007

XIAOLING WANG
Affiliation:
Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, Jiangsu, China. e-mail: [email protected]
WANG ZHOU
Affiliation:
Department of Statistics and Applied Probability, National University of Singapore, Singapore, 117546. e-mail: [email protected]

Abstract

Suppose that f(z) is a transcendental entire function and that the Fatou set F(f)≠∅. Setandwhere the supremum supU is taken over all components of F(f). If B1(f)<∞ or B2(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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2007

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