| Title:
|
Entire function sharing two polynomials with its $k$th derivative (English) |
| Author:
|
Majumder, Sujoy |
| Author:
|
Sarkar, Nabadwip |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
87-103 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate the uniqueness problem of entire functions that share two polynomials with their $k$th derivatives and obtain some results which improve and generalize the recent result due to Lü and Yi (2011). Also, we exhibit some examples to show that the conditions of our results are the best possible. (English) |
| Keyword:
|
meromorphic function |
| Keyword:
|
derivative |
| Keyword:
|
Nevanlinna theory |
| Keyword:
|
uniqueness |
| MSC:
|
30D35 |
| MSC:
|
30D45 |
| DOI:
|
10.21136/MB.2023.0017-22 |
| . |
| Date available:
|
2024-03-13T10:21:01Z |
| Last updated:
|
2024-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152295 |
| . |
| Reference:
|
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| Reference:
|
[2] Hayman, W. K.: Meromorphic Functions.Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). Zbl 0115.06203, MR 0164038 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Li, J., Yi, H.: Normal families and uniqueness of entire functions and their derivatives.Arch. Math. 87 (2006), 52-59. Zbl 1104.30019, MR 2246406, 10.1007/s00013-005-1619-0 |
| Reference:
|
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| Reference:
|
[7] Lü, F., Yi, H.: The Brück conjecture and entire functions sharing polynomials with their $k$-th derivatives.J. Korean Math. Soc. 48 (2011), 499-512. Zbl 1232.30024, MR 2815888, 10.4134/JKMS.2011.48.3.499 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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[11] Yang, C.-C., Yi, H.-X.: Uniqueness Theory of Meromorphic Functions.Mathematics and Its Applications (Dordrecht) 557. Kluwer Academic, Dordrecht (2003). Zbl 1070.30011, MR 2105668, 10.1007/978-94-017-3626-8 |
| Reference:
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| Reference:
|
[13] Zhang, J.-L., Yang, L.-Z.: A power of an entire function sharing one value with its derivative.Comput. Math. Appl. 60 (2010), 2153-2160. Zbl 1205.30033, MR 2719737, 10.1016/j.camwa.2010.08.001 |
| . |
