• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.69-91
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• 2022

In the paper we establish some new results depending on the comparative growth properties of composite transcendental entire and meromorphic functions using relative (p, q, t)L-th order, relative (p, q, t)L-th type and relative (p, q, t)L-th weak type and that of Wronskian generated by one of the factors.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.103-130
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• 2018

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*-order$, relative $_pL^*-lower$ order and differential monomials, differential polynomials generated by one of the factors.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.13-33
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• 2015

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.689-695
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• 2018

In this paper, we give some results on the zeros and fixed points of the difference and the divided difference of transcendental meromorphic functions. This improves on results of Langley.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.123-132
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• 2008

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.411-427
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• 2015

In this article, we main study the uniqueness problem of meromorphic function which difference polynomials sharing common values. We consider the entire function $(f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j})^{(k)}$ and the meromorphic function $f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j}$ to get the main results which extend Theorem 1.1 in paper[5] and theorem 1.4 in paper[6].

• 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 $t{\Delta}_qf$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1217-1227
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• 2018

In the paper, we study the growth and fixed point of solutions of high order linear differential equations with entire coefficients of [p, q]-order in the complex plane. We improve and extend some results due to T. B. Cao, J. F. Xu, Z. X. Chen, and J. Liu, J. Tu, L. Z. Shi.