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1
Content available remote

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).
2
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Analytic functions in the unit disc sharing values in a sector

100%
Xu H.-Y., Cao T.-B.
Annales Polonici Mathematici
|
2012
|
tom 103
|
nr 3
263-275
EN
We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).
3
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Zeros of solutions of certain higher order linear differential equations

100%
Xu H.-Y., Yi C.-F.
Annales Polonici Mathematici
|
2010
|
tom 97
|
nr 2
123-136
EN
We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $f^{(k)} + a_{k-1}(z)f^{(k-1)} + ⋯ + a₁(z)f' +D(z)f=0$, (1) where $D(z) = Q₁(z)e^{P₁(z)} + Q₂(z)e^{P₂(z)} + Q₃(z)e^{P₃(z)}$, P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z),$a_j(z)$ (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.
4
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Uniqueness of two analytic functions sharing four values in an angular domain

100%
Xu H.-Y., Cao T.-B.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 1
55-65
EN
We deal with the uniqueness problem for analytic functions sharing four distinct values in an angular domain and obtain some theorems which improve the result given by Cao and Yi [J. Math. Anal. Appl. 358 (2009)].
5
Content available remote

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.
6
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An improvement of Hayman's inequality on an angular domain

81%
Yi C.-F., Wang Y., Xu H.-Y.
Annales Polonici Mathematici
|
2010
|
tom 99
|
nr 2
181-192
EN
We investigate the properties of meromorphic functions on an angular domain, and obtain a form of Yang's inequality on an angular domain by reducing the coefficients of Hayman's inequality. Moreover, we also study Hayman's inequality in different forms, and obtain accurate estimates of sums of deficiencies.
7
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Some properties of solutions of complex q-shift difference equations

81%
Xu H.-Y., Tu J., Zheng X.-M.
Annales Polonici Mathematici
|
2013
|
tom 108
|
nr 3
289-304
EN
Combining difference and q-difference equations, we study the properties of meromorphic solutions of q-shift difference equations from the point of view of value distribution. We obtain lower bounds for the Nevanlinna lower order for meromorphic solutions of such equations. Our results improve and extend previous theorems by Zheng and Chen and by Liu and Qi. Some examples are also given to illustrate our results.
8
Content available remote

Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight

81%
Xu H.-Y., Yi C.-F., Cao T.-B.
Annales Polonici Mathematici
|
2009
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tom 95
|
nr 1
51-66
EN
This paper deals with the uniqueness problem for meromorphic functions sharing one value with finite weight. Our results generalize those of Fang, Hong, Bhoosnurmath and Dyavanal.
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