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1
Content available remote

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.
2
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On meromorphic functions for sharing two sets and three sets inm-punctured complex plane

81%
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.
3
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Results on the deficiencies of some differential-difference polynomials of meromorphic functions

81%
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).
4
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The generalized Laguerre inequalities and functions in the Laguerre-Pólya class

81%
Csordas G., Vishnyakova A.
Open Mathematics
|
2013
|
tom 11
|
nr 9
1643-1650
EN
The principal goal of this paper is to show that the various sufficient conditions for a real entire function, φ(x), to belong to the Laguerre-Pólya class (Definition 1.1), expressed in terms of Laguerre-type inequalities, do not require the a priori assumptions about the order and type of φ(x). The proof of the main theorem (Theorem 2.3) involving the generalized real Laguerre inequalities, is based on a beautiful geometric result, the Borel-Carathédodory Inequality (Theorem 2.1), and on a deep theorem of Lindelöf (Theorem 2.2). In case of the complex Laguerre inequalities (Theorem 3.2), the proof is sketched for it requires a slightly more delicate analysis. Section 3 concludes with some other cognate results, an open problem and a conjecture which is based on Cardon’s recent, ingenious extension of the Laguerre-type inequalities.
5
Content available remote

Uniqueness of meromorphic functions sharing two finite sets

81%
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.
6
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The uniqueness of meromorphic functions ink-punctured complex plane

81%
Xu H. Y., Liu S. Y.
Open Mathematics
|
2017
|
tom 15
|
nr 1
724-733
EN
The main purpose of this paper is to investigate the uniqueness of meromorphic functions that share two finite sets in the k-punctured complex plane. It is proved that there exist two sets S1, S2 with ♯S1 = 2 and ♯S2 = 5, such that any two admissible meromorphic functions f and g in Ω must be identical if EΩ(Sj, f) = EΩ(Sj, g)(j = 1,2).
7
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Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

62%
Luo L.-Q., Zheng X.-M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
970-976
EN
In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.
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