| 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:
|
http://hdl.handle.net/10338.dmlcz/143638 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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