• 대한수학회보
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• 제54권4호
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• pp.1159-1171
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• 2017

The purpose of this paper is twofold. The first is to show that two meromorphic functions f and g must be linked by a quasi-$M{\ddot{o}}bius$ transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-$M{\ddot{o}}bius$ transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by 4, where all zeros with multiplicities at least k > 865 are omitted. Moreover the explicit $M{\ddot{o}}bius$-transformation between such f and g is given. Our results are improvement of some recent results.

• 대한수학회보
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• 제46권6호
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• pp.1189-1200
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• 2009

The main purpose of this paper is to deal with the uniqueness of meromorphic functions sharing sets concerning small functions. We obtain two main theorems which improve and extend strongly some results due to R. Nevanlinna, Li-Qiao, Yao, Yi, Thai-Tan, and Cao-Yi.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.107-122
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• 2009

In this paper, we deal with the problem of uniqueness of meromorphic functions that share three values, and obtain some theorems which improve some results of Brosch, Yi and other authors.

• 대한수학회보
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• 제44권4호
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• pp.631-640
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• 2007

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.

• 대한수학회보
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• 제56권6호
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• pp.1511-1524
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• 2019

In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if f(z) and ${\Delta}_cf(z)$ share a(z), b(z), ${\infty}$ CM, where a(z), b(z)(${\neq}{\infty}$) are two distinct small functions of f(z), then $f(z){\equiv}{\Delta}_cf(z)$. The result improves the results due to Li et al. ([9]), Cui et al. ([1]) and $L{\ddot{u}}$ et al. ([12]).

• Kyungpook Mathematical Journal
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• 제50권1호
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• pp.71-80
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• 2010

In this paper, we deal with the uniqueness problems of meromorphic functions that share a small function with its derivative and improve some results of Yang, Yu, Lahiri, and Zhang, also answer some questions of T. D. Zhang and W. R. L$\"{u}$.

• Kyungpook Mathematical Journal
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• 제49권1호
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• pp.143-154
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• 2009

In this paper, we investigate uniqueness problems of meromorphic functions that share a small function with one of their derivatives, and give some results to improve some previous results.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.345-355
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• 2010

In this paper, we investigate uniqueness problems of meromorphic functions sharing a small function with their differential polynomials, and give some results which are related to a conjecture of R. Br$\"{u}$ck, and also improve several previous results.

• 대한수학회보
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• 제57권5호
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.

• 대한수학회보
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• 제58권4호
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).