• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.495-505
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• 2018

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.731-745
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• 2013

In this paper, we investigate uniqueness problems of certain types of $q$-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where $q$-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function $f$ and a non-zero complex constant $q$, $E(S_j,f)=E(S_j,{\Delta}_qf)$ for $j=1,2$ imply $f(z)=t{\Delta}_qf$, where $t^n=1$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $f(z)$ and $t{\Delta}_qf$.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.541-552
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• 2013

This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomials of moromorphic functions in this paper. In particular, we are interested in the existence of zeros of $f(z)^n({\lambda}f(z+c)^m+{\mu}f(z)^m)-a$, where f is a moromorphic function, n, m are two non-negative integers, and ${\lambda}$, ${\mu}$ are non-zero complex numbers. However, the proof here is obviously different to the one in [9]. We also study difference polynomials of entire functions sharing a common value, which improves the result in [10, 13].

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.235-243
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• 2009

In this paper, we deal with the problem of uniqueness of meromorphic functions that share two small functions with their derivatives, and obtain the following result which improves a result of Yao and Li: Let f(z) be a nonconstant meromorphic function, k > 5 be an integer. If f(z) and g(z) = $a_1(z)f(z)+a_2(z)f^{(k)}(z)$ share the value 0 CM, and share b(z) IM, $\overline{N}_E(r,f=0=F^{(k)})=S(r)$, f${\equiv}$g, where $a_1(z)$, $a_2(z)$ and b(z) are small functions of f(z).

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1175-1192
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• 2021

In this paper, we have studied on the uniqueness problems of meromorphic functions with its linear c-shift operator in the light of partial sharing. Our two results improve and generalize two very recent results of Noulorvang-Pham [Bull. Korean Math. Soc. 57 (2020), no. 5, 1083-1094] in some sense. In addition, our other results have improved and generalized a series of results due to Lü-Lü [Comput. Methods Funct. Theo. 17 (2017), no. 3, 395-403], Zhen [J. Contemp. Math. Anal. 54 (2019), no. 5, 296-301] and Banerjee-Bhattacharyya [Adv. Differ. Equ. 509 (2019), 1-23]. We have exhibited a number of examples to show that some conditions used in our results are essential.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.469-478
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• 2018

We prove some uniqueness theorems of nonconstant meromorphic functions partially sharing values with their shifts. As an application, we obtain a sufficient condition on periodic meromorphic functions. Moreover, some examples are given to illustrate that the conditions are sharp and necessary.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.467-481
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• 2016

We study the uniqueness question of transcendental meromorphic functions that share three values CM in some angular domains instead of the whole complex plane. The results in this paper extend the corresponding results in Zheng [13, 14] and Yi [12]. Some examples are given to show that the results in this paper, in a sense, are the best possible.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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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]).

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.249-261
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• 2022

Let f be a non-constant meromorphic function in the open complex plane ℂ. In this paper we prove under certain essential conditions that R(f) and P[f], rational function and differential polynomial of f respectively, share a small function of f and obtain a conclusion related to Brück conjecture. We give some examples in support to our result.

• International Journal of Contents
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• v.15 no.4
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• pp.74-81
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• 2019

This study examined the overall relationship between information privacy concern, need for uniqueness (NFU), and disclosure behavior to explain the personal factors that drive data-sharing on Facebook. The results of an online survey conducted with 222 Facebook users show that among diverse data that social media users disclose online, four distinct factors are identified: basic personal data, private data, personal opinions, and personal photos. In general, there is a negative relationship between privacy concern and a positive relationship between the NFU and the willingness to self-disclose information. Overall, the NFU was a better predictor of willingness to disclose information than privacy concern, gender, or age. While privacy concern has been identified as an influential factor when users evaluate social networking sites, the findings of this study contribute to the literature by demonstrating that an individual's need to manifest individualization on social media overrides privacy concerns.