| Title:
|
Entire functions sharing one finite value CM with their shifts and difference operators (English) |
| Author:
|
Miloudi, Boudaoud |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
4 |
| Year:
|
2026 |
| Pages:
|
649-666 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the uniqueness of an entire function $f(z)$ sharing one finite value CM with its shift and its difference operator, in each case we find that $f(z)=h(z)\beta ^{\alpha z/c}$, where $ \alpha \not =0,$ $\beta >1$ and $h(z)$ is a periodic entire function of period $c$. Here, we say that two entire functions $f(z)$ and $g(z)$ share a value $a$ CM if $f(z)-a$ and $g(z)-a$ have the same zeros with same multiplicities. (English) |
| Keyword:
|
uniqueness |
| Keyword:
|
entire function |
| Keyword:
|
difference operator |
| MSC:
|
30D35 |
| DOI:
|
10.21136/MB.2025.0047-25 |
| . |
| Date available:
|
2026-09-23T08:25:51Z |
| Last updated:
|
2026-09-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153772 |
| . |
| Reference:
|
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| Reference:
|
[2] Chen, B., Li, S.: Uniqueness problems on entire functions that share a small function with their difference operators.Adv. Difference Equ. 2014 (2014), Article ID 311, 11 pages. Zbl 1417.30018, MR 3360566, 10.1186/1687-1847-2014-311 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J.: Uniqueness of meromorphic functions sharing values with their shifts.Complex Var. Elliptic Equ. 56 (2011), 81-92. Zbl 1217.30029, MR 2774582, 10.1080/17476930903394770 |
| Reference:
|
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| Reference:
|
[7] Latreuch, Z., Farissi, A. El, Belaïdi, B.: Entire functions sharing small functions with their difference operators.Electron. J. Differ. Equ. 2015 (2015), Article ID 132, 10 pages. Zbl 1320.30058, MR 3358504 |
| Reference:
|
[8] Li, S., Gao, Z.: Entire functions sharing one or two finite values CM with their shifts or difference operators.Arch. Math. 97 (2011), 475-483. Zbl 1243.30068, MR 2860575, 10.1007/s00013-011-0324-4 |
| Reference:
|
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| Reference:
|
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| . |
