• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.365-371
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• 2016

Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$, which states as following inequality, for positive integers $n{\geq}2$, $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$.

• 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]).

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.729-741
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• 2021

We mainly study the value distributions of L-functions in the extended selberg class. Concerning weighted sharing, we prove an uniqueness theorem when certain differential monomial of a meromorphic function share a polynomial with certain differential monomial of an L-function which improve and generalize some recent results due to Liu, Li and Yi [11], Hao and Chen [3] and Mandal and Datta [12].

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.17-51
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• 2019

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.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.495-512
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• 2021

We study the value distribution theory of L-functions and completely resolve a question from Yang [10]. This question is related to L-functions sharing three finite values with meromorphic functions. The main result in this paper extends corresponding results from Li [10].

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1145-1155
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• 2019

Let f be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a quantitative estimations of the characteristic function T(r, f) in terms of the counting function of a homogeneous differential polynomial generated by f. Our result improves and generalizes some recent results.

• 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.

• 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.

• East Asian mathematical journal
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• v.13 no.2
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• pp.213-219
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• 1997

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.911-927
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• 2019

Let $\mathscr{B}^{{\eta},{\mu}}_{p,n}\;({\alpha});\;({\eta},{\mu}{\in}{\mathbb{R}},\;n,\;p{\in}{\mathbb{N}})$ denote all functions f class in the unit disk ${\mathbb{U}}$ as $f(z)=z^p+\sum_{k=n+p}^{\infty}a_kz^k$ which satisfy: $$\|\[{\frac{f^{\prime}(z)}{pz^{p-1}}}\]^{\eta}\;\[\frac{z^p}{f(z)}\]^{\mu}-1\| <1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. And $\mathscr{M}^{{\eta},{\mu}}_{p,n}\;({\alpha})$ indicates all meromorphic functions h in the punctured unit disk $\mathbb{U}^*$ as $h(z)=z^{-p}+\sum_{k=n-p}^{\infty}b_kz^k$ which satisfy: $$\|\[{\frac{h^{\prime}(z)}{-pz^{-p-1}}}\]^{\eta}\;\[\frac{1}{z^ph(z)}\]^{\mu}-1\|<1-{\frac{\alpha}{p}};\;(z{\in}{\mathbb{U}},\;0{\leq}{\alpha}<p)$$. In this paper several sufficient conditions for some classes of functions are investigated. The authors apply Jack's Lemma, to obtain this conditions. Furthermore, sufficient conditions for strongly starlike and convex p-valent functions of order ${\gamma}$ and type ${\beta}$, are also considered.