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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. Meromorphic functions that share a nonzero polynomial IM
- Creator:
- Sahoo, Pulak
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- uniqueness, meromorphic function, and differential polynomials
- Language:
- English
- Description:
- We study the uniqueness theorems of meromorphic functions concerning differential polynomials sharing a nonzero polynomial IM, and obtain two theorems which will supplement two recent results due to X. M. Li and L. Gao.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. Nonlinear differential monomials sharing two values
- Creator:
- Majumder, Sujoy
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- uniqueness, meromorphic function, weighted sharing, and nonlinear differential polynomials
- Language:
- English
- Description:
- Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely h nh (k) (h = f, g) sharing a nonzero polynomial of degree less than or equal to 3 with finite weight have common poles and obtain two results. The results in this paper significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. Nonlinear differential polynomials sharing a non-zero polynomial with finite weight
- Creator:
- Banerjee, Abhijit and Ahamed, Molla Basir
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- uniqueness, meromorphic function, and nonlinear differential polynomial
- Language:
- English
- Description:
- In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely h n (h − 1)m (h = f, g), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of the sharing non-zero polynomial or when the first derivative is taken under consideration, better conclusions can be obtained.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. On the generalization of two results of Cao and Zhang
- Creator:
- Majumder, Sujoy
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- uniqueness, meromorphic function, weighted sharing, and nonlinear differential polynomials
- Language:
- English
- Description:
- This paper studies the uniqueness of meromorphic functions f n ∏ k i=1 (f (i) ) ni and g n ∏ k i=1 (g (i) ) ni that share two values, where n, nk, k ∈ N, ni ∈ N ∪ {0}, i = 1, 2, . . . , k − 1. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
7. Properties of differences of meromorphic functions
- Creator:
- Chen, Zong-Xuan and Zhon, Kwang Ho
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- meromorphic function, difference, divided difference, zero, and fixed point
- Language:
- English
- Description:
- Let $f$ be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference $g(z)=f(z+c)-f(z)$ and the divided difference $g(z)/f(z)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
8. 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