On the value distribution of f2f(k)
2005 ◽
Vol 78
(1)
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pp. 17-26
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Keyword(s):
AbstractIn this paper, we prove that for a transcendental meromorphic function f(z) on the complex plane, the inequality T(r, f) < 6N (r, 1/(f2 f(k)−1)) + S(r, f) holds, where k is a positive integer. Moreover, we prove the following normality criterion: Let ℱ be a family of meromorphic functions on a domain D and let k be a positive integer. If for each ℱ ∈ ℱ, all zeros of ℱ are of multiplicity at least k, and f2 f(k) ≠ 1 for z ∈ D, then ℱ is normal in the domain D. At the same time we also show that the condition on multiple zeros of f in the normality criterion is necessary.
2004 ◽
Vol 47
(1)
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pp. 152-160
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2008 ◽
Vol 51
(3)
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pp. 697-709
2009 ◽
Vol 139
(5)
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pp. 1091-1099
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1997 ◽
Vol 62
(3)
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pp. 398-404