Title:
|
A note on some results of Li and Li (English) |
Author:
|
Majumder, Sujoy |
Author:
|
Saha, Somnath |
Language:
|
English |
Journal:
|
Mathematica Bohemica |
ISSN:
|
0862-7959 (print) |
ISSN:
|
2464-7136 (online) |
Volume:
|
143 |
Issue:
|
3 |
Year:
|
2018 |
Pages:
|
277-289 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The purpose of the paper is to study the uniqueness problems of linear differential polynomials of entire functions sharing a small function and obtain some results which improve and generalize the related results due to J. T. Li and P. Li (2015). Basically we pay our attention to the condition $\lambda (f)\not =1$ in Theorems 1.3, 1.4 from J. T. Li and P. Li (2015). Some examples have been exhibited to show that conditions used in the paper are sharp. (English) |
Keyword:
|
entire function |
Keyword:
|
linear differential polynomial |
Keyword:
|
uniqueness |
MSC:
|
30D35 |
idZBL:
|
Zbl 06940884 |
idMR:
|
MR3852295 |
DOI:
|
10.21136/MB.2017.0106-16 |
. |
Date available:
|
2018-08-31T09:43:25Z |
Last updated:
|
2020-07-01 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147393 |
. |
Reference:
|
[1] Banerjee, A.: Meromorphic functions sharing one value.Int. J. Math. Math. Sci. 22 (2005), 3587-3598. Zbl 1093.30024, MR 2205158, 10.1155/IJMMS.2005.3587 |
Reference:
|
[2] Hayman, W. K.: Meromorphic Functions.Oxford Mathematical Monographs. Clarendon Press, Oxford (1964). Zbl 0115.06203, MR 0164038 |
Reference:
|
[3] Herold, H.: Differentialgleichungen im Komplexen.Studia Mathematica. Skript 2. Vandenhoeck & Ruprecht, Göttingen (1975). Zbl 03505407, MR 0470293 |
Reference:
|
[4] Hua, X. H.: A unicity theorem for entire functions.Bull. Lond. Math. Soc. 22 (1990), 457-462. Zbl 0714.30030, MR 1082015, 10.1112/blms/22.5.457 |
Reference:
|
[5] Lahiri, I.: Uniqueness of meromorphic functions as governed by their differential polynomials.Yokohama Math. J. 44 (1997), 147-156. Zbl 0884.30023, MR 1453358 |
Reference:
|
[6] 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:
|
[7] Laine, I.: Nevanlinna Theory and Complex Differential Equations.De Gruyter Studies in Mathematics 15. Walter de Gruyter, Berlin (1993). Zbl 0784.30002, MR 1207139 |
Reference:
|
[8] Li, J.-T., Li, P.: Uniqueness of entire functions concerning differential polynomials.Commun. Korean Math. Soc. 30 (2015), 93-101. Zbl 1320.30059, MR 3346483, 10.4134/CKMS.2015.30.2.093 |
Reference:
|
[9] Mues, E., Reinders, M.: On a question of C. C. Yang.Complex Variables, Theory Appl. 34 (1997), 171-179. Zbl 0948.30036, MR 1473597, 10.1080/17476939708815045 |
Reference:
|
[10] Shibazaki, K.: Unicity theorems for entire functions of finite order.Mem. Natl. Def. Acad. 21 (1981), 67-71. Zbl 0507.30022, MR 1262958 |
Reference:
|
[11] Yang, C. C.: On two entire functions which together with their first derivatives have the same zeros.J. Math. Anal. Appl. 56 (1976), 1-6. Zbl 0338.30018, MR 0419761, 10.1016/0022-247X(76)90002-0 |
Reference:
|
[12] Yang, C. C., Yi, H. X.: On the unicity theorem for meromorphic functions with deficient values.Acta Math. Sin. 37 (1994), 62-72 Chinese. Zbl 0804.30026, MR 1272506 |
Reference:
|
[13] Yang, C. C., Yi, H. X.: Uniqueness Theory of Meromorphic Functions.Mathematics and Its Applications 557. Kluwer Academic Publishers, Dordrecht (2003). Zbl 1070.30011, MR 2105668 |
Reference:
|
[14] Yi, H. X.: A question of C. C. Yang on the uniqueness of entire functions.Kodai Math. J. 13 (1990), 39-46. Zbl 0707.30022, MR 1047593, 10.2996/kmj/1138039158 |
Reference:
|
[15] Yi, H. X.: Uniqueness of meromorphic functions and a question of C. C. Yang.Complex Variables, Theory Appl. 14 (1990), 169-176. Zbl 0701.30025, MR 1048716, 10.1080/17476939008814415 |
Reference:
|
[16] Yi, H. X.: Meromorphic functions that share one or two values.Complex Variables, Theory Appl. 28 (1995), 1-11. Zbl 0841.30027, MR 1700258, 10.1080/17476939508814833 |
Reference:
|
[17] Zhang, J.-L., Yang, L.-Z.: Some results related to a conjecture of R. Brück.JIPAM J. Inequal. Pure Appl. Math. 8 (2007), Article No. 18, 11 pages. Zbl 1136.30009, MR 2295712 |
. |