• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.461-473
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• 2023

Let f be a nonconstant meromorphic function of hyper-order strictly less than 1, and let c ∈ ℂ \ {0} such that f(z + c) ≢ f(z). We prove that if f and its exact difference ∆_cf(z) = f(z + c) - f(z) share partially 0, ∞ CM and share 1 IM, then ∆_cf = f, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.607-622
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• 2007

We prove four theorems on the uniqueness of non linear differential polynomials sharing one value which improve a result of Yang and Hua, and supplements some results of Lahiri, Xu and Qiu and Banerjee.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1105-1117
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• 2022

In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of Pⁿ(C) where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.39-50
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• 2018

In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.765-780
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• 2023

In this paper, we explore the uniqueness property between the transcendental meromorphic functions and differential polynomial. With the notion of weighted sharing, we generalised the many previous results on uniqueness property. Here we discussed the uniqueness of [P(f)(αf^m + β)^s]^(k) - η(z) and [P(g)(αg^m + β)^s]^(k) - η(z). Meanwhile, we generalised the result of Harina P. waghamore and Rajeshwari S[1].

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1401-1422
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• 2015

Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1181-1203
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• 2018

In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.195-204
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• 2011

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.865-870
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• 2018

We show that if two nonconstant meromorphic functions f and g on $\mathbb{C}$ sharing some finite sets IM, then there is a nonconstant rational function R(z) such that R(f) = R(g).

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.653-666
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• 2015

With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author.