| Title:
|
Nonlinear differential polynomials sharing a small function (English) |
| Author:
|
Banerjee, Abhijit |
| Author:
|
Mukherjee, Sonali |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
41-56 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1]. (English) |
| Keyword:
|
meromorphic function |
| Keyword:
|
uniqueness |
| Keyword:
|
nonlinear differential polynomials |
| Keyword:
|
small function |
| Keyword:
|
weakly weighted sharing |
| MSC:
|
30D35 |
| idZBL:
|
Zbl 1212.30113 |
| idMR:
|
MR2431230 |
| . |
| Date available:
|
2008-06-06T22:52:43Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108095 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/119772 |
| . |
| Reference:
|
[1] Banerjee, A.: On uniqueness for nonlinear differential polynomials sharing the same $1$-point.Ann. Polon. Math. 89 (3) (2006), 259–272. Zbl 1104.30018, MR 2262553, 10.4064/ap89-3-3 |
| Reference:
|
[2] Fang, C. Y., Fang, M. L.: Uniqueness of meromorphic functions and differential polynomials.Comput. Math. Appl. 44 (5–6) (2002), 607–617. Zbl 1035.30018, MR 1925805, 10.1016/S0898-1221(02)00175-X |
| Reference:
|
[3] Fang, M. L., Hong, W.: A unicity theorem for entire functions concerning differential polynomials.Indian J. Pure Appl. Math. 32 (9) (2001), 1343–1348. Zbl 1005.30023, MR 1875450 |
| Reference:
|
[4] Frank, G., Reinders, M.: A unique range set for meromorphic functions with 11 elements.Complex Variables Theory Appl. 37 (9) (1998), 185–193. Zbl 1054.30519, MR 1687880, 10.1080/17476939808815132 |
| Reference:
|
[5] Hayman, W. K.: Meromorphic Functions.The Clarendon Press, Oxford, 1964. Zbl 0115.06203, MR 0164038 |
| Reference:
|
[6] Lahiri, I.: Uniqueness of meromorphic functions when two linear differential polynomials share the same $1$-points.Ann. Polon. Math. 71 (2) (1999), 113–128. Zbl 0938.30022, MR 1703886 |
| Reference:
|
[7] Lahiri, I.: Value distribution of certain differential polynomials.Internat. J. Math. Math. Sci. 28 (2) (2001), 83–91. Zbl 0999.30023, MR 1885054, 10.1155/S0161171201011036 |
| Reference:
|
[8] Lahiri, I.: Weighted sharing and uniqueness of meromorphic functions.Nagoya Math. J. 161 (2001), 193–206. Zbl 0981.30023, MR 1820218 |
| 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] Lahiri, I., Banerjee, A.: Weighted sharing of two sets.Kyungpook Math. J. 46 (1) (2006), 79–87. Zbl 1103.30017, MR 2214802 |
| Reference:
|
[11] Lahiri, I., Pal, R.: Nonlinear differential polynomials sharing $1$-points.Bull. Korean Math. Soc. 43 (1) (2006), 161–168. Zbl 1183.30028, MR 2204868, 10.4134/BKMS.2006.43.1.161 |
| Reference:
|
[12] Lahiri, I., Sarkar, A.: Nonlinear differential polynomials sharing $1$-points with weight two.Chinese J. Contemp. Math. 25 (3) (2004), 325–334. Zbl 1069.30051, MR 2159311 |
| Reference:
|
[13] Lin, S., Lin, W. C.: Uniqueness of meromorphic functions concerning weakly weighted sharing.Kodai Math. J. 29 (2006), 269–280. Zbl 1126.30018, MR 2247436, 10.2996/kmj/1151936441 |
| Reference:
|
[14] Lin, W. C.: Uniqueness of differential polynomials and a problem of Lahiri.Pure Appl. Math. 17 (2) (2001), 104–110, (in Chinese). MR 1848848 |
| Reference:
|
[15] Lin, W. C., Yi, H. X.: Uniqueness theorems for meromorphic function.Indian J. Pure Appl. Math. 35 (2) (2004), 121–132. Zbl 1056.30031, MR 2040726 |
| Reference:
|
[16] Lin, W. C., Yi, H. X.: Uniqueness theorems for meromorphic functions concerning fixed points.Complex Variables Theory Appl. 49 (11) (2004), 793–806. Zbl 1067.30065, MR 2097218, 10.1080/02781070412331298624 |
| Reference:
|
[17] Mohon’ko, A. Z.: On the Nevanlinna characteristics of some meromorphic functions. Theory of Functions.Funct. Anal. Appl. 14 (1971), 83–87. |
| Reference:
|
[18] Yang, C. C.: On deficiencies of differential polynomials II.Math. Z. 125 (1972), 107–112. Zbl 0217.38402, MR 0294642 |
| Reference:
|
[19] Yi, H. X.: Uniqueness of meromorphic functions and a question of C. C. Yang.Complex Variables Theory Appl. 14 (14) (1990), 169–176. Zbl 0701.30025, MR 1048716, 10.1080/17476939008814415 |
| Reference:
|
[20] Yi, H. X.: On characteristic function of a meromorphic function and its derivative.Indian J. Math. 33 (2) (1991), 119–133. Zbl 0799.30018, MR 1140875 |
| Reference:
|
[21] Yi, H. X.: Meromorphic functions that share one or two values.Complex Variables Theory Appl. 28 (1995), 1–11. Zbl 0841.30027, 10.1080/17476939508814833 |
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