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Title: Uniqueness of entire functions concerning difference polynomials (English)
Author: Meng, Chao
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 139
Issue: 1
Year: 2014
Pages: 89-97
Summary lang: English
Category: math
Summary: In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let $f(z)$ and $g(z)$ be two transcendental entire functions of finite order, and $\alpha (z)$ a small function with respect to both $f(z)$ and $g(z)$. Suppose that $c$ is a non-zero complex constant and $n\geq 7$ (or $n\geq 10$) is an integer. If $f^{n}(z)(f(z)-1)f(z+c)$ and $g^{n}(z)(g(z)-1)g(z+c)$ share “$(\alpha (z),2)$” (or $(\alpha (z),2)^{*}$), then $f(z)\equiv g(z)$. Our results extend and generalize some well known previous results. (English)
Keyword: entire function
Keyword: difference polynomial
Keyword: uniqueness
MSC: 30D35
MSC: 39A05
idZBL: Zbl 06362244
idMR: MR3231431
DOI: 10.21136/MB.2014.143638
Date available: 2014-03-20T08:31:35Z
Last updated: 2020-07-29
Stable URL:
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