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Title: Uniqueness and two shared set problems of meromorphic functions in a different angle (English)
Author: Mallick, Sanjay
Author: Banerjee, Abhijit
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 146
Issue: 1
Year: 2021
Pages: 19-45
Summary lang: English
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Category: math
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Summary: The purpose of the paper is to represent the two shared set problems in an elaborative and convenient manner. In the main result of the paper, we have exhaustively treated the two shared set problem on the open complex plane. As a consequence of the main result, we have investigated the same problem in a different perspective, which has yet not been studied. Further, two examples have been exhibited in the paper to show the sharpness of some of these results. (English)
Keyword: meromorphic function
Keyword: uniqueness
Keyword: weighted sharing
Keyword: shared set
MSC: 30D35
idZBL: 07332740
idMR: MR4227309
DOI: 10.21136/MB.2019.0063-18
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Date available: 2021-03-12T16:18:22Z
Last updated: 2021-04-19
Stable URL: http://hdl.handle.net/10338.dmlcz/148745
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Reference: [1] Banerjee, A.: Some uniqueness results on meromorphic functions sharing three sets.Ann. Pol. Math. 92 (2007), 261-274. Zbl 1130.30027, MR 2353890, 10.4064/ap92-3-5
Reference: [2] Banerjee, A.: On the uniqueness of meromorphic functions that share two sets.Georgian Math. J. 15 (2008), 21-38. Zbl 1159.30018, MR 2418873, 10.1515/GMJ.2008.21
Reference: [3] Banerjee, A.: On the uniqueness of meromorphic functions sharing two sets.Commun. Math. Anal. 9 (2010), 1-11. Zbl 1195.30042, MR 2737750
Reference: [4] Banerjee, A.: Bi-unique range sets for meromorphic functions.Nihonkai Math. J. 24 (2013), 121-134. Zbl 1291.30189, MR 3178503
Reference: [5] Banerjee, A.: Corrigendum to ``Bi-unique range sets for meromorphic functions''.Nihonkai Math. J. 26 (2015), 71-74. Zbl 06566363, MR 3482758
Reference: [6] Banerjee, A., Bhattacharjee, P.: Uniqueness and set sharing of derivatives of meromorphic functions.Math. Slovaca 61 (2011), 197-214. Zbl 1265.30141, MR 2786694, 10.2478/s12175-011-0005-6
Reference: [7] Banerjee, A., Majumder, S., Mukherjee, S.: A uniqueness result on meromorphic functions sharing two sets II.Fasc. Math. 53 (2014), 17-30. Zbl 1331.30018, MR 3331510
Reference: [8] Banerjee, A., Mallick, S.: On the characterisations of a new class of strong uniqueness polynomials generating unique range sets.Comput. Methods Funct. Theory 17 (2017), 19-45 erratum ibid. 17 2017 page 735. Zbl 1364.30035, MR 3620877, 10.1007/s40315-016-0174-y
Reference: [9] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets.Am. J. Math. 122 (2000), 1175-1203. Zbl 0983.30013, MR 1797660, 10.1353/ajm.2000.0045
Reference: [10] Gross, F.: Factorization of meromorphic functions and some open problems.Complex Analysis. Lect. Notes Math. 599 Springer, Berlin (1977), 51-67 J. D. Buckholtz et al. Zbl 0357.30007, MR 0450529, 10.1007/bfb0096825
Reference: [11] Han, Q., Yi, H.-X.: Some further results on meromorphic functions that share two sets.Ann. Pol. Math. 93 (2008), 17-31. Zbl 1160.30016, MR 2383339, 10.4064/ap93-1-2
Reference: [12] Lahiri, I.: Value distribution of certain differential polynomials.Int. J. Math. Math. Sci. 28 (2001), 83-91. Zbl 0999.30023, MR 1885054, 10.1155/S0161171201011036
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] Lin, W.-C., Yi, H.-X.: Some further results on meromorphic functions that share two sets.Kyungpook Math. J. 43 (2003), 73-85. Zbl 1064.30023, MR 1961610
Reference: [16] Yang, C. C.: On deficiencies of differential polynomials. II.Math. Z. 125 (1972), 107-112. Zbl 0217.38402, MR 0294642, 10.1007/BF01110921
Reference: [17] Yi, B., Li, Y.: Uniqueness of meromorphic functions that share two sets with CM.Acta Math. Sin., Chin. Ser. 55 Chinese (2012), 363-368. Zbl 1265.30162, MR 2963005
Reference: [18] Yi, H.-X.: Uniqueness of meromorphic functions and question of Gross.Sci. China, Ser. A 37 (1994), 802-813. Zbl 0821.30024, MR 1324763
Reference: [19] Yi, H.-X.: Meromorphic functions that share two sets.Acta Math. Sin. 45 (2002), 75-82 Chinese. Zbl 1092.30051, MR 1923666
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