Bounded Fatou components of transcendental entire functions with order less than 1/2 |
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| Authors: | Cun Ji Yang Yu Hua Li |
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| Institution: | 1. Department of Mathematics and Computer Sciences, Dali University, Dali 671003, P. R. China;
2. Department of Mathematics, Yunnan Normal University, Kunming 650092, P. R. China |
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| Abstract: | Let f be a transcendental entire function with order ρ<1/2 and let ρ be a sufficiently large constant. We prove that if there exists r0>1 such that, for all r>r0 and any small ε>0,
M(rσ, f)≥M(r, f)σ+ε,
then every component of the Fatou set F(f) is bounded. |
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| Keywords: | Transcendental entire function small growth Fatou component bounded |
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