• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.545-562
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• 2022

Using the conception of weakly weighted sharing we discussed the value distribution of the differential product functions constructed with a polynomial and difference operator of entire function. Here we established two uniqueness result on product of difference operators when two such functions share a small function.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.439-449
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• 2019

In 2006, S. Lin and W. Lin introduced the definition of weakly weighted-sharing of meromorphic functions which is between "CM" and "IM". In this paper, using the notion of weakly weighted-sharing, we study the uniqueness of nonconstant homogeneous differential polynomials P[f] and P[g] generated by meromorphic functions f and g, respectively. Our results generalize the results due to S. Lin and W. Lin, and H.-Y. Xu and Y. Hu.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.549-565
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• 2024

In this paper, we investigate the uniqueness of linear difference differential polynomials sharing a small function. By using the concepts of weakly weighted and relaxed weighted sharing of transcendental entire functions with finite order, we obtained the corresponding results, which improve and extend some results of Chao Meng [14].

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.651-666
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• 2009

With the aid of weakly weighted sharing and a recently introduced sharing notion in [3] known as relaxed weighted sharing we investigate the uniqueness of meromorphic functions sharing a small function with its differential polynomials. Our results will improve and supplement all the results obtained by Zhang and Yang [17] as well as a substantial part of the results recently obtained by the present author [2] and thus provide a better answer to the questions posed by Yu [14] in this regard.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.529-542
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• 2017

In this paper, using the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain differential polynomials sharing a small function. The results obtained in this paper extend the theorem obtained by Jianren Long [9].

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.37-50
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• 2022

The purpose of the paper is to study the uniqueness problems of certain type of difference polynomials sharing a small function. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo and G. Biswas [Tamkang Journal of Mathematics, 49(2)(2018), 85-97].

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].