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Unbounded domains of normality of entire functions of small growth

Published online by Cambridge University Press:  01 March 2000

ZHENG JIAN-HUA
ZHENG JIAN-HUA
Affiliation:
Department of Applied Mathematics, Tsinghua University, Beijing, P.R. China
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Abstract

Let f: C → C denote a transcendental entire function and let m(r, f) equal min {[mid ]f(z)[mid ][ratio ][mid ]z[mid ] = r}. In this note, we mainly prove that if

formula here

then the set of normality N(f) of f has no unbounded preperiodic and periodic components. In particular, f has no Baker domains. We also discuss non-existence of unbounded components of normality under other conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 128 , Issue 2 , March 2000 , pp. 355 - 361
Copyright
© The Cambridge Philosophical Society 2000

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