Previous |  Up |  Next

Article

Title: On a result of Zhang and Xu concerning their open problem (English)
Author: Majumder, Sujoy
Author: Mandal, Rajib
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 54
Issue: 2
Year: 2018
Pages: 65-89
Summary lang: English
.
Category: math
.
Summary: The motivation of this paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial with the help of the idea of normal family. The result of the paper improves and generalizes the recent result due to Zhang and Xu [24]. Our another remarkable aim is to solve an open problem as posed in the last section of [24]. (English)
Keyword: normal families
Keyword: uniqueness
Keyword: meromorphic function
Keyword: small functions
MSC: 30D30
MSC: 30D35
idZBL: Zbl 06890306
idMR: MR3813736
DOI: 10.5817/AM2018-2-65
.
Date available: 2018-06-05T11:59:18Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/147214
.
Reference: [1] Banerjee, A.: On a question of Gross.J. Math. Anal. Appl. 327 (2) (2007), 1273–1283. Zbl 1115.30029, MR 2280003, 10.1016/j.jmaa.2006.04.078
Reference: [2] Banerjee, A.: Uniqueness of certain nonlinear differential polynomials sharing 1-points.Kyungpook Math. J. 51 (2011), 43–58. MR 2784645, 10.5666/KMJ.2011.51.1.043
Reference: [3] Chang, J.M., Zalcman, L.: Meromorphic functions that share a set with their derivatives.J. Math. Anal. Appl. 338 (2008), 1191–1205. MR 2386477, 10.1016/j.jmaa.2007.05.079
Reference: [4] Fang, M.L., Qiu, H.L.: 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: [5] Frank, G.: Eine Vermutung Von Hayman über Nullslellen meromorphic Funktion.Math. Z. 149 (1976), 29–36. 10.1007/BF01301627
Reference: [6] Hayman, W.K.: Picard values of meromorphic functions and their derivatives.Ann. of Math. (2) 70 (1959). Zbl 0088.28505
Reference: [7] Hayman, W.K.: Meromorphic Functions.The Clarendon Press, Oxford, 1964. Zbl 0115.06203
Reference: [8] Lahir, I., Banerjee, A.: Weighted sharing of two sets.Kyungpook Math. J. 46 (2006). MR 2214802
Reference: [9] Lahiri, I.: Value distribution of certain differential polynomials.Internat. J. Math. Math. Sci. 28 (2001), 83–91. Zbl 0999.30023, MR 1885054, 10.1155/S0161171201011036
Reference: [10] 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: [11] 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: [12] 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: [13] Majumder, S.: On an open problem of Xiao-Bin Zhang and Jun-Feng Xu.Demonstratio Math. 49 (2) (2016), 161–182. MR 3507931
Reference: [14] Pang, X.C.: Normality conditions for differential polynomials.Kexue Tongbao (Chinese) 33 (1988), 1690–1693.
Reference: [15] Schiff, J.: Normal families.Berlin, 1993.
Reference: [16] Xu, J.F., Lü, F., Yi, H.X.: Fixed points and uniqueness of meromorphic functions.Comput. Math. Appl. 59 (2010), 9–17. MR 2575487, 10.1016/j.camwa.2009.07.024
Reference: [17] Yamanoi, K.: The second main theorem for small functions and related problems.Acta Math. 192 (2004), 225–294. Zbl 1203.30035, MR 2096455, 10.1007/BF02392741
Reference: [18] Yang, C.C.: On deficiencies of differential polynomials II.Math. Z. 125 (1972), 107–112. Zbl 0217.38402, 10.1007/BF01110921
Reference: [19] Yang, C.C., Hua, X.H.: Uniqueness and value sharing of meromorphic functions.Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406. Zbl 0890.30019
Reference: [20] Yang, C.C., Yi, H.X.: Uniqueness Theory of Meromorphic Functions.Kluwer Academic Publishers, Dordrecht/Boston/London, 2003. Zbl 1070.30011, MR 2105668
Reference: [21] Zalcman, L.: A heuristic principle in complex theory.Amer. Math. Monthly 82 (1975), 813–817. 10.1080/00029890.1975.11993942
Reference: [22] Zalcman, L.: Normal families, new perspectives.Bull. Amer. Math. Soc. 35 (1998), 215–230. 10.1090/S0273-0979-98-00755-1
Reference: [23] Zhang, Q.C.: Meromorphic function that shares one small function with its derivative.J. Inequal. Pure Appl. Math. 6 (4) (2005), Art.116 online http://jipam.vu.edu.au/. Zbl 1097.30033, MR 2178297
Reference: [24] Zhang, X.B., Xu, J.F.: Uniqueness of meromorphic functions sharing a small function and its applications.Comput. Math. Appl. 61 (2011), 722–730. MR 2764068, 10.1016/j.camwa.2010.12.022
.

Files

Files Size Format View
ArchMathRetro_054-2018-2_1.pdf 601.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo