Startseite Derivatives of meromorphic functions sharing two sets with least cardinalities
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Derivatives of meromorphic functions sharing two sets with least cardinalities

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Veröffentlicht/Copyright: 8. August 2018
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Abstract

In this paper, we prove two theorems establishing the uniqueness of the derivatives of meromorphic functions f(k) and g(k) when they share two sets with least cardinalities. Our results improve some existing results of Fang–Lahiri, Banerjee–Bhattacharjee, Banerjee–Mallick and Banerjee–Chakraborty.

MSC 2010: 30D35

Award Identifier / Grant number: UGC(ERO)PSW-163/15-16

Funding statement: The author was supported by the University Grants Commission (UGC(ERO)PSW-163/15-16).

References

[1] A. Banerjee and P. Bhattacharjee, Uniqueness of derivatives of meromorphic functions sharing two or three sets, Turkish J. Math. 34 (2010), no. 1, 21–34. 10.3906/mat-0806-7Suche in Google Scholar

[2] A. Banerjee and P. Bhattacharjee, Uniqueness and set sharing of derivatives of meromorphic functions, Math. Slovaca 61 (2011), no. 2, 197–214. 10.2478/s12175-011-0005-6Suche in Google Scholar

[3] A. Banerjee and B. Chakraborty, Further results on the uniqueness of meromorphic functions and their derivative counterpart sharing one or two sets, Jordan J. Math. Stat. 9 (2016), no. 2, 117–139. Suche in Google Scholar

[4] A. Banerjee and S. Mallick, On the bi unique range sets for derivatives of meromorphic functions, Surv. Math. Appl. 10 (2015), 95–111. Suche in Google Scholar

[5] M.-L. Fang and I. Lahiri, Unique range set for certain meromorphic functions, Indian J. Math. 45 (2003), no. 2, 141–150. Suche in Google Scholar

[6] F. Gross, Factorization of meromorphic functions and some open problems, Complex Analysis (Lexington 1976), Lecture Notes in Math. 599, Springer, Berlin (1977), 51–69. 10.1007/BFb0096825Suche in Google Scholar

[7] F. Gross and C. C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 17–20. 10.3792/pjaa.58.17Suche in Google Scholar

[8] W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. Suche in Google Scholar

[9] I. Lahiri, The range set of meromorphic derivatives, Northeast. Math. J. 14 (1998), no. 3, 353–360. Suche in Google Scholar

[10] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. 10.1017/S0027763000027215Suche in Google Scholar

[11] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), no. 3, 241–253. 10.1080/17476930108815411Suche in Google Scholar

[12] I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno) 38 (2002), no. 2, 119–128. Suche in Google Scholar

[13] I. Lahiri and A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J. 44 (2004), no. 4, 575–584. Suche in Google Scholar

[14] I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), no. 1, 79–87. Suche in Google Scholar

[15] W.-C. Lin and H.-X. Yi, Some further results on meromorphic functions that share two sets, Kyungpook Math. J. 43 (2003), no. 1, 73–85. Suche in Google Scholar

[16] H. Yi and W. Lü, Meromorphic functions that share two sets. II, Acta Math. Sci. Ser. B (Engl. Ed.) 24 (2004), no. 1, 83–90. 10.1016/S0252-9602(17)30363-6Suche in Google Scholar

[17] H. X. Yi, Uniqueness of meromorphic functions and question of Gross, Sci. China Ser. A 37 (1994), no. 7, 802–813. Suche in Google Scholar

[18] H.-X. Yi, Unicity theorems for meromorphic or entire functions. III, Bull. Aust. Math. Soc. 53 (1996), no. 1, 71–82. 10.1017/S0004972700016737Suche in Google Scholar

[19] H.-X. Yi, Meromorphic functions that share one or two values. II, Kodai Math. J. 22 (1999), no. 2, 264–272. 10.2996/kmj/1138044046Suche in Google Scholar

[20] H. X. Yi, Meromorphic functions that share two sets, Acta Math. Sinica (Chin. Ser.) 45 (2002), no. 1, 75–82. 10.2996/kmj/1138043751Suche in Google Scholar

[21] H.-X. Yi and W.-C. Lin, Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J. 46 (2006), no. 3, 437–444. Suche in Google Scholar

Received: 2017-06-06
Revised: 2018-03-09
Accepted: 2018-07-11
Published Online: 2018-08-08
Published in Print: 2019-07-01

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