http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
THE UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE DIFFERENTIAL POLYNOMIALS SHARE SOME VALUES
MENG, CHAO,LI, XU The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If f<sup>n</sup>(f<sup>3</sup> - 1)f′ and g<sup>n</sup>(g<sup>3</sup> - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).
The uniqueness of meromorphic functions whose differential polynomials share some values
Chao Meng,Xu Li 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let $f$ and $g$ be two nonconstant meromorphic functions, $n\geq 12$ a positive integer. If $f^{n}(f^{3}-1)f'$ and $g^{n}(g^{3}-1)g'$ share $(1,2)$, $f$ and $g$ share $\infty$ IM, then $f\equiv g$. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).
Entire Functions and Their Derivatives Share Two Finite Sets
Meng, Chao,Hu, Pei-Chu Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.3
In this paper, we study the uniqueness of entire functions and prove the following theorem. Let n(${\geq}$ 5), k be positive integers, and let $S_1$ = {z : $z^n$ = 1}, $S_2$ = {$a_1$, $a_2$, ${\cdots}$, $a_m$}, where $a_1$, $a_2$, ${\cdots}$, $a_m$ are distinct nonzero constants. If two non-constant entire functions f and g satisfy $E_f(S_1,2)$ = $E_g(S_1,2)$ and $E_{f^{(k)}}(S_2,{\infty})$ = $E_{g^{(k)}}(S_2,{\infty})$, then one of the following cases must occur: (1) f = tg, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = t{$a_1$, $a_2$, ${\cdots}$, $a_m$}, where t is a constant satisfying $t^n$ = 1; (2) f(z) = $de^{cz}$, g(z) = $\frac{t}{d}e^{-cz}$, {$a_1$, $a_2$, ${\cdots}$, $a_m$} = $(-1)^kc^{2k}t\{\frac{1}{a_1},{\cdots},\frac{1}{a_m}\}$, where t, c, d are nonzero constants and $t^n$ = 1. The results in this paper improve the result given by Fang (M.L. Fang, Entire functions and their derivatives share two finite sets, Bull. Malaysian Math. Sc. Soc. 24(2001), 7-16).
UNIQUENESS OF CERTAIN TYPES OF DIFFERENCE POLYNOMIALS
MENG, CHAO,ZHAO, LIANG The Korean Society for Computational and Applied M 2018 Journal of applied mathematics & informatics Vol.36 No.5
In this paper, we investigate the uniqueness problems of certain types of difference polynomials sharing a small function. The results of the paper improve and generalize the recent results due to H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13], P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44].
UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING THE SHIFTS AND DERIVATIVES
MENG, CHAO,LIU, GANG The Korean Society for Computational and Applied M 2019 Journal of applied mathematics & informatics Vol.37 No.1
This paper is devoted to studying the sharing value problem for the derivative of a meromorphic function with its shift and q-difference. The results in the paper improve and generalize the recent result due to Qi, Li and Yang.
UNIQUENESS OF CERTAIN TYPES OF DIFFERENCE POLYNOMIALS
Chao Meng,Liang Zhao 한국전산응용수학회 2018 Journal of applied mathematics & informatics Vol.36 No.5
In this paper, we investigate the uniqueness problems of certain types of dierence polynomials sharing a small function. The results of the paper improve and generalize the recent results due to H.P. Waghamore [Tbilisi Math. J. 11(2018), 1-13], P. Sahoo and B. Saha [App. Math. E-Notes. 16(2016), 33-44].
UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING THE SHIFTS AND DERIVATIVES
CHAO MENG,Gang Liu 한국전산응용수학회 2019 Journal of applied mathematics & informatics Vol.37 No.1
This paper is devoted to studying the sharing value problem for the derivative of a meromorphic function with its shift and q-dierence. The results in the paper improve and generalize the recent result due to Qi, Li and Yang [28].
UNIQUENESS FOR THE POWER OF A MEROMORPHIC FUNCTION
MENG, CHAO,LI, AND XU The Korean Society for Computational and Applied M 2017 Journal of applied mathematics & informatics Vol.35 No.1
In this paper, we investigate the uniqueness problem related to the power of a meromorphic functions sharing a small function with its derivative. The results in this paper improve and generalize some well known previous results.
UNIQUENESS FOR THE POWER OF A MEROMORPHIC FUNCTION
CHAO MENG,XU LI 한국전산응용수학회 2017 Journal of applied mathematics & informatics Vol.35 No.1
In this paper, we investigate the uniqueness problem related to the power of a meromorphic functions sharing a small function with its derivative. The results in this paper improve and generalize some well known previous results.
Normal Families and Shared Values of Meromorphic Functions
Meng, Chao Department of Mathematics 2008 Kyungpook mathematical journal Vol.48 No.2
Some criteria for determining the normality of the family F of meromorphic functions in the unit disc, which share values depending on f $\in$ F with their derivatives is obtained. The new results in this paper improve some earlier related results given by Pang and Zalcman [3], Fang and Zalcman [2], A. P. Singh and A. Singh [5].