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1. Further investigation ''On an open problem of Zhang and Xu''

Creator:
Majumder, Sujoy
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
uniqueness, meromorphic function, small function, and nonlinear differential polynomial
Language:
English
Description:
The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The result of the paper improves and generalizes the recent results due to X. B. Zhang and J. F. Xu (2011). We also solve an open problem posed in the last section of X. B. Zhang and J. F. Xu (2011).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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