Uniformly bounded components of normality
نویسندگان
چکیده
Suppose that f(z) is a transcendental entire function and that the Fatou set F (f) 6= ∅. Set B1(f) := sup U supz∈U log(|z| + 3) infw∈U log(|w|+ 3) and B2(f) := sup U supz∈U log log(|z|+ 30) infw∈U log(|w| + 3) , where 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. In this article, we will show that, under some conditions, F (f) is (strongly) uniformly bounded.
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