Normal functions and normal families.
A note on some results of Schwick.
On the value distribution of .
Normality criterion concerning sharing functions. II.
On the normal meromorphic functions.
Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.
Uniqueness of transcendental meromorphic functions with their nonlinear differential polynomials sharing the small function.
On the five-point theorems due to Lappan
By using an extension of the spherical derivative introduced by Lappan, we obtain some results on normal functions and normal families, which extend Lappan's five-point theorems and Marty's criterion, and improve some previous results due to Li and Xie, and the author. Also, another proof of Lappan's theorem is given.
Uniqueness of entire or meromorphic functions sharing one value or a function with finite weight.
On the Nevanlinna direction of quasi-meromorphic mapping dealing with multiple values.
Oscillation of solutions of some higher order linear differential equations.
Weighted sharing and uniqueness of entire functions
In this paper we study the uniqueness for meromorphic functions sharing one value, and obtain some results which improve and generalize the related results due to M. L. Fang, X. Y. Zhang, W. C. Lin, T. D. Zhang, W. R. Lü and others.
On the value distribution of differential polynomials of meromorphic functions
Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and , where R ≢ 0 is a rational function and P is a polynomial, and let be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and , then has infinitely many zeros.
Normality criteria and multiple values II
Let ℱ be a family of meromorphic functions defined in a domain D, let ψ (≢ 0, ∞) be a meromorphic function in D, and k be a positive integer. If, for every f ∈ ℱ and z ∈ D, (1) f≠ 0, ; (2) all zeros of have multiplicities at least (k+2)/k; (3) all poles of ψ have multiplicities at most k, then ℱ is normal in D.
The uniqueness of meromorphic functions ink-punctured complex plane
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
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 ′ ) <+∞, 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
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
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
We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation , (1) where , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.
Uniqueness theorems for meromorphic functions that share three sets with weights.
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