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2. Meromorphic function sharing a small function with a linear differential polynomial

Creator:
Lahiri, Indrajit and Sarkar, Amit
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
meromorphic function, differential polynomial, small function, and sharing
Language:
English
Description:
The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the following result: Let f be a nonconstant meromorphic function and L a nonconstant linear differential polynomial generated by f. Suppose that a = a(z) (6≡ 0,∞) is a small function of f. If f − a and L− a share 0 CM and (k + 1)N(r,∞; f) + N(r, 0; f ′ ) + Nk(r, 0; f ′ ) < λT (r, f′ ) + S(r, f′ ) for some real constant λ ∈ (0, 1), then f − a = (1 + c/a)(L − a), where c is a constant and 1 + c/a 6≡ 0.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Uniqueness and differential polynomials of meromorphic functions sharing a nonzero polynomial

Creator:
Sahoo, Pulak
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
uniqueness, meromorphic function, differential polynomial, and weighted sharing
Language:
English
Description:
Let k be a nonnegative integer or infinity. For a ∈ C ∪ {∞} we denote by Ek(a; f) the set of all a-points of f where an a-point of multiplicity m is counted m times if m ≤ k and k + 1 times if m > k. If Ek(a; f) = Ek(a; g) then we say that f and g share the value a with weight k. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Weighted sharing and uniqueness of entire functions

Creator:
Wu, Fengqin and Xu, Yan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
entire function, weighted sharing, differential polynomial, and uniqueness
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public