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THE BRÜCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR κ-TH DERIVATIVES
Lu, Feng,Yi, Hongxun Korean Mathematical Society 2011 대한수학회지 Vol.48 No.3
The purpose of this paper is twofold. The first is to establish a uniqueness theorem for entire function sharing two polynomials with its ${\kappa}$-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Br$\"{u}$-ck conjecture with the idea of sharing polynomial.
THE BRUCK CONJECTURE AND ENTIRE FUNCTIONS SHARING POLYNOMIALS WITH THEIR k-TH DERIVATIVES
Feng Lu,Hongxun Yi 대한수학회 2011 대한수학회지 Vol.48 No.3
The purpose of this paper is twofold. The rst is to establish a uniqueness theorem for entire function sharing two polynomials with its k-th derivative, by using the theory of normal families. Meanwhile, the theorem generalizes some related results of Rubel and Yang and of Li and Yi. Several examples are provided to show the conditions are necessary. The second is to generalize the Bruck conjecture with the idea of sharing polynomial.
Uniqueness of Entire Functions and Differential Polynomials
Junfeng Xu,Hongxun Yi 대한수학회 2007 대한수학회보 Vol.44 No.4
In this paper, we study the uniqueness of entire functionsand prove the following result: Let f and g be two nonconstant entirefunctions,n;m be positive integers. Iffn (fm 1)f0 and gn (gm 1)g0share 1 IM and n > 4m + 11, then f g. The result improves the resultof Fang-Fang.
UNIQUENESS OF ENTIRE FUNCTIONS AND DIFFERENTIAL POLYNOMIALS
Xu, Junfeng,Yi, Hongxun Korean Mathematical Society 2007 대한수학회보 Vol.44 No.4
In this paper, we study the uniqueness of entire functions and prove the following result: Let f and g be two nonconstant entire functions, n, m be positive integers. If $f^n(f^m-1)f#\;and\;g^n(g^m-1)g#$ share 1 IM and n>4m+11, then $f{\equiv}g$. The result improves the result of Fang-Fang.
Uniqueness of Meromorphic Functions Concerning the Difference Polynomials
LIU, FANGHONG,YI, HONGXUN Department of Mathematics 2015 Kyungpook mathematical journal Vol.55 No.2
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].