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1
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On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

100%
Xu H.-Y., Zheng X.-M., Wang H.
Open Mathematics
|
2016
|
tom 14
|
nr 1
913-924
EN
In this article, we study the uniqueness problem of meromorphic functions in m-punctured complex plane Ω and obtain that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 9, such that any two admissible meromorphic functions f and g in Ω must be identical if f, g share S1, S2 I M in Ω.
2
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Results on the deficiencies of some differential-difference polynomials of meromorphic functions

100%
Zheng X.-M., Xu H.-Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
100-108
EN
In this paper, we study the relation between the deficiencies concerning a meromorphic function f(z), its derivative f′(z) and differential-difference monomials f(z)mf(z+c)f′(z), f(z+c)nf′(z), f(z)mf(z+c). The main results of this paper are listed as follows: Let f(z) be a meromorphic function of finite order satisfying lim sup r→+∞ T(r, f) T(r,  f ′ ) <+∞, $$\mathop {\lim \,{\rm sup}}\limits_{r \to + \infty } {{T(r,\,f)} \over {T(r,\,f')}}{\rm{ < }} + \infty ,$$ and c be a non-zero complex constant, then δ(∞, f(z)m f(z+c)f′(z))≥δ(∞, f′) and δ(∞,f(z+c)nf′(z))≥ δ(∞, f′). We also investigate the value distribution of some differential-difference polynomials taking small function a(z) with respect to f(z).
3
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Normality and shared sets of meromorphic functions

100%
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.
4
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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.
5
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Value distributions of solutions to complex linear differential equations in angular domains

100%
Zhang G.
Open Mathematics
|
2017
|
tom 15
|
nr 1
884-894
EN
In this paper we study the iterated order and oscillations of the solutions to some complex linear differential equations in angular domains. Our theorems improve some recent results.
6
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Meromorphic functions of infinite order in the angular domain

88%
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.
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