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On the uniqueness of a power of a meromorphic function sharing a small function with the power of its derivative

Abhijit Banerjee, Sujoy Majumder (2010)

Commentationes Mathematicae Universitatis Carolinae

In the paper we discuss the uniqueness of the n -th power of a meromorphic function sharing a small function with the power of its k -th derivative and improve and supplement a result of Zhang-Lü [Complex Var. Elliptic Equ. 53 (2008), no. 9, 857–867]. We also rectify one recent result obtained by Chen and Zhang in [Kyungpook Math. J. 50 (2010), no. 1, 71–80] dealing with a question posed by T.D. Zhang and W.R. Lü in [Complex Var. Elliptic Equ. 53 (2008), no. 9, 857–867].

On the uniqueness of an entire function sharing a small entire function with some linear differential polynomial

Xiao-Min Li, Hong-Xun Yi (2009)

Czechoslovak Mathematical Journal

We prove a theorem on the growth of nonconstant solutions of a linear differential equation. From this we obtain some uniqueness theorems concerning that a nonconstant entire function and its linear differential polynomial share a small entire function. The results in this paper improve many known results. Some examples are provided to show that the results in this paper are the best possible.

On the uniqueness of meromorphic functions that share three sets

Abhijit Banerjee (2009)

Mathematica Bohemica

With the aid of the notion of weighted sharing and pseudo sharing of sets we prove three uniqueness results on meromorphic functions sharing three sets, all of which will improve a result of Lin-Yi in Complex Var. Theory Appl. (2003).

On the value distribution of differential polynomials of meromorphic functions

Yan Xu, Huiling Qiu (2010)

Annales Polonici Mathematici

Let f be a transcendental meromorphic function of infinite order on ℂ, let k ∈ ℕ and φ = R e P , where R ≢ 0 is a rational function and P is a polynomial, and let a , a , . . . , a k - 1 be holomorphic functions on ℂ. If all zeros of f have multiplicity at least k except possibly finitely many, and f = 0 f ( k ) + a k - 1 f ( k - 1 ) + + a f = 0 , then f ( k ) + a k - 1 f ( k - 1 ) + + a f - φ has infinitely many zeros.

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