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Uniqueness of meromorphic functions sharing two finite sets

100%
Chen J.-F.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1244-1250
EN
We prove uniqueness theorems of meromorphic functions, which show how two meromorphic functions are uniquely determined by their two finite shared sets. This answers a question posed by Gross. Moreover, some examples are provided to demonstrate that all the conditions are necessary.
2
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Normality criteria for families of zero-free meromorphic functions

100%
Chen J.-F.
Annales Polonici Mathematici
|
2015
|
tom 115
|
nr 1
89-98
EN
Let ℱ be a family of zero-free meromorphic functions in a domain D, let n, k and m be positive integers with n ≥ m+1, and let a ≠ 0 and b be finite complex numbers. If for each f ∈ ℱ, $f^m + a(f^{(k)})ⁿ - b$ has at most nk zeros in D, ignoring multiplicities, then ℱ is normal in D. The examples show that the result is sharp.
3
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Meromorphic functions of infinite order in the angular domain

100%
Chen J.-F.
Open Mathematics
|
2012
|
tom 10
|
nr 3
1103-1112
EN
We investigate the value distribution of meromorphic functions in the angular domain. In particular, we show a close relationship between radially distributed values and Borel directions of transcendental meromorphic functions of infinite order in some angular domains.
4
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Normality and shared sets of meromorphic functions

63%
Lin G.-B., Chen J.-F.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1312-1316
EN
The purpose of this paper is to investigate the normal families and shared sets of meromorphic functions. The results obtained complement the related results due to Fang, Liu and Pang.
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