• 대한수학회보
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• 제48권2호
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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.

• 대한수학회보
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• 제55권1호
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• pp.205-226
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• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.995-1002
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• 2022

In this paper, we study the uniqueness of meromorphic functions sharing a unique range sets Ignoring multiplicities. This paper improves the result of Pulak sahoo and Anjan Sarkar [15].

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.121-133
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• 2018

The purpose of the paper is to study the meromorphic functions sharing a nonzero polynomial with finite weight. The results of the paper improve and generalize the recent results due to Pulak Sahoo and Sajahan Seikh [9].

• Korean Journal of Mathematics
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• 제18권4호
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• pp.465-472
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• 2010

In this paper, we investigate the extent of the set on which the modulus of a meromorphic function is lower bounded by a term related to some Nevanlinna Theory functionals. A. I. Shcherba estimate the size of the set on which the modulus of an entire function is lower bounded by 1. Our theorem in this paper shows that the same result holds in the case that the lower bound is replaced by$lT(r,f)$, $0{\leq}l$ < 1, which improves Shcherba's result. We also give a similar estimation for meromorphic functions.

• 대한수학회보
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• 제50권4호
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• pp.1209-1219
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• 2013

In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it's first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br$\ddot{u}$ck conjecture with the idea of sharing functions.

• 대한수학회보
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• 제50권5호
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• pp.1471-1479
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• 2013

In this paper, we study the non-existence of finite order entire solutions of nonlinear differential-difference of the form $$f^n+Q(z,f)=h$$, where $n{\geq}2$ is an integer, $Q(z,f)$ is a differential-difference polynomial in $f$ with polynomial coefficients, and $h$ is a meromorphic function of order ${\leq}1$.

• 대한수학회보
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• 제45권3호
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• pp.427-435
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• 2008

In this paper we consider the problem of whether certain homogeneous or non-homogeneous differential polynomials in f(z) necessarily have infinitely many zeros. Particularly, this extends a result of Gopalakrishna and Bhoosnurmath [3, Theorem 2] for a general differential polynomial of degree $\bar{d}$(P) and lower degree $\underline{d}$(P).

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.169-180
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• 2006

This paper proves the following results: Let $f$ be a transcendental entire function, and let $k({\geq})2$ be a positive integer. If $T(r,\;f){\neq}N_{1)}(r,1/f)+S(r,\;f)$, then $ff^{(k)}$ assumes every finite nonzero value infinitely often. Also the case when f is a transcendental meromorphic function has been considered and some results are obtained.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.