| Title:
|
Meromorphic function sharing a small function with a linear differential polynomial (English) |
| Author:
|
Lahiri, Indrajit |
| Author:
|
Sarkar, Amit |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
1-11 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The problem of uniqueness of an entire or a meromorphic function when it shares a value or a small function with its derivative became popular among the researchers after the work of Rubel and Yang (1977). Several authors extended the problem to higher order derivatives. Since a linear differential polynomial is a natural extension of a derivative, in the paper we study the uniqueness of a meromorphic function that shares one small function CM with a linear differential polynomial, and prove the following result: Let $f$ be a nonconstant meromorphic function and $L$ a nonconstant linear differential polynomial generated by $f$. Suppose that $a = a(z)$ ($\not \equiv 0, \infty $) is a small function of $f$. If $f-a$ and $L-a$ share $0$ CM and \[ (k+1)\overline N(r, \infty ; f)+ \overline N(r, 0; f')+ N_{k}(r, 0; f')< \lambda T(r, f')+ S(r, f') \] for some real constant $\lambda \in (0, 1)$, then $ f-a=(1+ {c}/{a})(L-a)$, where $c$ is a constant and $1+{c}/{a} \not \equiv 0$. (English) |
| Keyword:
|
meromorphic function |
| Keyword:
|
differential polynomial |
| Keyword:
|
small function |
| Keyword:
|
sharing |
| MSC:
|
30D35 |
| idZBL:
|
Zbl 06562155 |
| idMR:
|
MR3475134 |
| DOI:
|
10.21136/MB.2016.1 |
| . |
| Date available:
|
2016-03-17T19:39:13Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144846 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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