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### The uniqueness of meromorphic functions ink-punctured complex plane

Open Mathematics

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).

### Results on the deficiencies of some differential-difference polynomials of meromorphic functions

Open Mathematics

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 ′ ) <+∞, $\underset{r\to +\infty }{lim\phantom{\rule{0.166667em}{0ex}}\mathrm{sup}}\frac{T\left(r,\phantom{\rule{0.166667em}{0ex}}f\right)}{T\left(r,\phantom{\rule{0.166667em}{0ex}}{f}^{\text{'}}\right)}<+\infty ,$ 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...

### Uniqueness of two analytic functions sharing four values in an angular domain

Annales Polonici Mathematici

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)].

### Analytic functions in the unit disc sharing values in a sector

Annales Polonici Mathematici

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).

### Zeros of solutions of certain higher order linear differential equations

Annales Polonici Mathematici

We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation ${f}^{\left(k\right)}+{a}_{k-1}\left(z\right){f}^{\left(k-1\right)}+\cdots +a₁\left(z\right){f}^{\text{'}}+D\left(z\right)f=0$, (1) where $D\left(z\right)=Q₁\left(z\right){e}^{P₁\left(z\right)}+Q₂\left(z\right){e}^{P₂\left(z\right)}+Q₃\left(z\right){e}^{P₃\left(z\right)}$, P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z),${a}_{j}\left(z\right)$ (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

### Uniqueness results of meromorphic functions whose nonlinear differential polynomials have one nonzero pseudo value

Matematički Vesnik

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

Open Mathematics

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.

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

Annales Polonici Mathematici

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.

### An improvement of Hayman's inequality on an angular domain

Annales Polonici Mathematici

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.

### Some properties of solutions of complex q-shift difference equations

Annales Polonici Mathematici

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.

### Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function.

International Journal of Mathematics and Mathematical Sciences

### Uniqueness of entire or meromorphic functions sharing one value or a function with finite weight.

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

### On the Nevanlinna direction of quasi-meromorphic mapping dealing with multiple values.

Applied Mathematics E-Notes [electronic only]

### Oscillation of solutions of some higher order linear differential equations.

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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