| Title:
|
A power of a meromorphic function sharing two small functions with a derivative of the power (English) |
| Author:
|
Indrajit, Lahiri |
| Author:
|
Majumder, Sujoy |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
4 |
| Year:
|
2022 |
| Pages:
|
485-502 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In connection to a conjecture of W. Lü, Q. Li and C. Yang (2014), we prove a result on small function sharing by a power of a meromorphic function with few poles with a derivative of the power. Our results improve a number of known results. (English) |
| Keyword:
|
meromorphic function |
| Keyword:
|
derivative |
| Keyword:
|
small function |
| MSC:
|
30D35 |
| idZBL:
|
Zbl 07655822 |
| idMR:
|
MR4512169 |
| DOI:
|
10.21136/MB.2021.0121-20 |
| . |
| Date available:
|
2022-11-16T11:16:42Z |
| Last updated:
|
2023-04-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151094 |
| . |
| Reference:
|
[1] Brück, R.: On entire functions which share one value CM with their first derivative.Result. Math. 30 (1996), 21-24. Zbl 0861.30032, MR 1402421, 10.1007/BF03322176 |
| Reference:
|
[2] Cao, T.: On the Brück conjecture.Bull. Aust. Math. Soc. 93 (2016), 248-259. Zbl 1379.30016, MR 3480935, 10.1017/S000497271500115X |
| Reference:
|
[3] Chen, Z.-X., Shon, K. H.: On conjecture of R. Brück concerning the entire function sharing one value CM with its derivative.Taiwanese J. Math. 8 (2004), 235-244. Zbl 1062.30032, MR 2061691, 10.11650/twjm/1500407625 |
| Reference:
|
[4] Clunie, J.: On integral and meromorphic functions.J. Lond. Math. Soc. 37 (1962), 17-27. Zbl 0104.29504, MR 0143906, 10.1112/jlms/s1-37.1.17 |
| Reference:
|
[5] Frank, G.: Eine Vermutung von Hayman über Nullslellen meromorpher Funktionen.Math. Z. 149 (1976), 29-36 German. Zbl 0312.30032, MR 0422615, 10.1007/BF01301627 |
| Reference:
|
[6] Gundersen, G. G., Yang, L.-Z.: Entire functions that share one value with one or two of their derivatives.J. Math. Anal. Appl. 223 (1998), 88-95. Zbl 0911.30022, MR 1627356, 10.1006/jmaa.1998.5959 |
| Reference:
|
[7] Hayman, W. K.: Meromorphic Functions.Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). Zbl 0115.06203, MR 0164038 |
| Reference:
|
[8] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions.Nagoya Math. J. 161 (2001), 193-206. Zbl 0981.30023, MR 1820218, 10.1017/S0027763000027215 |
| Reference:
|
[9] Lahiri, I.: Weighted value sharing and uniqueness of meromorphic functions.Complex Variables, Theory Appl. 46 (2001), 241-253. Zbl 1025.30027, MR 1869738, 10.1080/17476930108815411 |
| Reference:
|
[10] Lin, S., Lin, W.: Uniqueness of meromorphic functions concerning weakly weighted-sharing.Kodai Math. J. 29 (2006), 269-280. Zbl 1105.30017, MR 2247436, 10.2996/kmj/1151936441 |
| Reference:
|
[11] 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:
|
[12] Lü, W., Li, Q., Yang, C.: On the transcendental entire solutions of a class of differential equations.Bull. Korean Math. Soc. 51 (2014), 1281-1289. Zbl 1300.30063, MR 3267229, 10.4134/BKMS.2014.51.5.1281 |
| Reference:
|
[13] Majumder, S.: A result on a conjecture of W. Lü, Q. Li and C. Yang.Bull. Korean Math. Soc. 53 (2016), 411-421. Zbl 1343.30025, MR 3483447, 10.4134/BKMS.2016.53.2.411 |
| Reference:
|
[14] Yang, C.-C., Yi, H.-X.: Uniqueness Theory of Meromorphic Functions.Mathematics and Its Applications (Dordrecht) 557. Kluwer Academic Publishers, Dordrecht (2003). Zbl 1070.30011, MR 2105668, 10.1007/978-94-017-3626-8 |
| Reference:
|
[15] Yang, L.-Z., Zhang, J.-L.: Non-existence of meromorphic solutions of Fermat type functional equation.Aequationes Math. 76 (2008), 140-150. Zbl 1161.30022, MR 2443466, 10.1007/s00010-007-2913-7 |
| Reference:
|
[16] Zhang, J.: Meromorphic functions sharing a small function with their derivatives.Kyungpook Math. J. 49 (2009), 143-154. Zbl 1177.30040, MR 2527380, 10.5666/KMJ.2009.49.1.143 |
| Reference:
|
[17] Zhang, J., Yang, L.: A power of a meromorphic function sharing a small function with its derivative.Ann. Acad. Sci. Fenn., Math. 34 (2009), 249-260. Zbl 1177.30041, MR 2489025 |
| Reference:
|
[18] 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 |
| . |
