| Title:
|
Nonlinear differential monomials sharing two values (English) |
| Author:
|
Majumder, Sujoy |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
339-361 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely $\smash {h^{n}h^{(k)}}$ $(h=f,g)$ sharing a nonzero polynomial of degree less than or equal to $3$ with finite weight have common poles and obtain two results. The results in this paper significantly rectify, improve and generalize the results due to Cao and Zhang (2012). (English) |
| Keyword:
|
uniqueness |
| Keyword:
|
meromorphic function |
| Keyword:
|
weighted sharing |
| Keyword:
|
nonlinear differential polynomials |
| MSC:
|
30D35 |
| idZBL:
|
Zbl 06644018 |
| idMR:
|
MR3557584 |
| DOI:
|
10.21136/MB.2016.0080-13 |
| . |
| Date available:
|
2016-10-01T16:02:21Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145898 |
| . |
| Reference:
|
[1] Alzahary, T. C., Yi, H. X.: Weighted value sharing and a question of I. Lahiri.Complex Variables, Theory Appl. 49 (2004), 1063-1078. Zbl 1067.30055, MR 2111304, 10.1080/02781070410001701074 |
| Reference:
|
[2] Banerjee, A.: On uniqueness for nonlinear differential polynomials sharing the same 1-point.Ann. Pol. Math. 89 (2006), 259-272. Zbl 1104.30018, MR 2262553, 10.4064/ap89-3-3 |
| Reference:
|
[3] Banerjee, A.: Meromorphic functions sharing one value.Int. J. Math. Math. Sci. 2005 (2005), 3587-3598. Zbl 1093.30024, MR 2205158, 10.1155/IJMMS.2005.3587 |
| Reference:
|
[4] Bergweiler, W., Eremenko, A.: On the singularities of the inverse to a meromorphic function of finite order.Rev. Mat. Iberoam. 11 (1995), 355-373. Zbl 0830.30016, MR 1344897, 10.4171/RMI/176 |
| Reference:
|
[5] Cao, Y.-H., Zhang, X.-B.: Uniqueness of meromorphic functions sharing two values.J. Inequal. Appl. (electronic only) 2012 (2012), Article ID 100, 10 pages. Zbl 1291.30193, MR 2946490 |
| Reference:
|
[6] Chen, H. H., Fang, M. L.: On the value distribution of $f^{n}f'$.Sci. China Ser. A. 38 (1995), 789-798. MR 1360682 |
| Reference:
|
[7] Dou, J., Qi, X.-G., Yang, L.-Z.: Entire functions that share fixed-points.Bull. Malays. Math. Sci. Soc. (2) 34 (2011), 355-367. Zbl 1216.30033, MR 2788409 |
| Reference:
|
[8] Fang, M., Hua, X.: Entire functions that share one value.J. Nanjing Univ., Math. Biq. 13 (1996), 44-48. Zbl 0899.30022, MR 1411806 |
| Reference:
|
[9] Fang, M., Qiu, H.: Meromorphic functions that share fixed-points.J. Math. Anal. Appl. 268 (2002), 426-439. Zbl 1030.30028, MR 1896207, 10.1006/jmaa.2000.7270 |
| Reference:
|
[10] Frank, G.: Eine Vermutung von Hayman über Nullstellen meromorpher Funktionen.Math. Z. 149 German (1976), 29-36. MR 0422615 |
| Reference:
|
[11] Hayman, W. K.: Meromorphic Functions.Oxford Mathematical Monographs Clarendon Press, Oxford (1964). Zbl 0115.06203, MR 0164038 |
| Reference:
|
[12] K{ö}hler, L.: Meromorphic functions sharing zeros and poles and also some of their derivatives sharing zeros.Complex Variables, Theory Appl. 11 (1989), 39-48. Zbl 0637.30029, MR 0998240, 10.1080/17476938908814322 |
| Reference:
|
[13] 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:
|
[14] 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:
|
[15] Lahiri, I., Dewan, S.: Value distribution of the product of a meromorphic function and its derivative.Kodai Math. J. 26 (2003), 95-100. Zbl 1077.30025, MR 1966685, 10.2996/kmj/1050496651 |
| Reference:
|
[16] Lahiri, I., Sahoo, P.: Uniqueness of non-linear differential polynomials sharing 1-points.Georgian Math. J. 12 (2005), 131-138. Zbl 1073.30022, MR 2136891 |
| Reference:
|
[17] Lahiri, I., Sarkar, A.: Nonlinear differential polynomials sharing 1-points with weight two.Chin. J. Contemp. Math. 25 (2004), 325-334. Zbl 1069.30051, MR 2159311 |
| Reference:
|
[18] Lin, W. C.: Uniqueness of differential polynomials and a problem of Lahiri.Pure Appl. Math. 17 Chinese (2001), 104-110. MR 1848848 |
| Reference:
|
[19] Xu, J.-F., Lü, F., Yi, H.-X.: Fixed-points and uniqueness of meromorphic functions.Comput. Math. Appl. 59 (2010), 9-17. Zbl 1189.30069, MR 2575487, 10.1016/j.camwa.2009.07.024 |
| Reference:
|
[20] Xu, J., Yi, H., Zhang, Z.: Some inequalities of differential polynomials.Math. Inequal. Appl. 12 (2009), 99-113. Zbl 1169.30314, MR 2489354 |
| Reference:
|
[21] Yang, C.-C.: On deficiencies of differential polynomials. II.Math. Z. 125 (1972), 107-112. Zbl 0217.38402, MR 0294642, 10.1007/BF01110921 |
| Reference:
|
[22] Yang, C.-C., Hua, X.: Uniqueness and value-sharing of meromorphic functions.Ann. Acad. Sci. Fenn., Math. 22 (1997), 395-406. Zbl 0890.30019, MR 1469799 |
| Reference:
|
[23] Yang, L.: Value Distribution Theory.Translated and revised from the 1982 Chinese original Springer, Berlin; Beijing, Science Press (1993). Zbl 0790.30018, MR 1301781 |
| Reference:
|
[24] Yi, H. X.: On characteristic function of a meromorphic function and its derivative.Indian J. Math. 33 (1991), 119-133. Zbl 0799.30018, MR 1140875 |
| Reference:
|
[25] Zhang, J.: Uniqueness theorems for entire functions concerning fixed points.Comput. Math. Appl. 56 (2008), 3079-3087. Zbl 1165.30362, MR 2474563, 10.1016/j.camwa.2008.07.006 |
| Reference:
|
[26] Zhang, Q.: Meromorphic function that shares one small function with its derivative.\mbox{JIPAM}, J. Inequal. Pure Appl. Math. (electronic only) 6 (2005), Article No. 116, 13 pages. Zbl 1097.30033, MR 2178297 |
| Reference:
|
[27] Zhang, X.-Y., Lin, W.-C.: Uniqueness and value-sharing of entire functions.J. Math. Anal. Appl. 343 (2008), 938-950. Zbl 1152.30034, MR 2417114, 10.1016/j.jmaa.2008.02.011 |
| Reference:
|
[28] Zhang, T., Lü, W.: Uniqueness theorems on meromorphic functions sharing one value.Comput. Math. Appl. 55 (2008), 2981-2992. Zbl 1142.30330, MR 2401445, 10.1016/j.camwa.2007.11.029 |
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