Tbilisi Mathematical Journal

Bi-unique range sets with smallest cardinalities for the derivatives of meromorphic functions

Abhijit Banerjee and Sanjay Mallick

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Abstract

Inspired by the advent of bi-unique range sets [2], we obtain a new bi-unique range sets, with smallest cardinalities ever for the derivatives of meromorphic functions which improves all the results obtained so far in some sense including a result of Banerjee-Bhattacharjee [4]. Furthermore at the last section we pose an open question for future research.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 2 (2016), 1-13.

Dates
Received: 29 October 2015
Accepted: 20 June 2016
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769063

Digital Object Identifier
doi:10.1515/tmj-2016-0015

Mathematical Reviews number (MathSciNet)
MR3538509

Zentralblatt MATH identifier
1350.30045

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory

Keywords
Meromorphic function Uniqueness Shared set Weighted sharing

Citation

Banerjee, Abhijit; Mallick, Sanjay. Bi-unique range sets with smallest cardinalities for the derivatives of meromorphic functions. Tbilisi Math. J. 9 (2016), no. 2, 1--13. doi:10.1515/tmj-2016-0015. https://projecteuclid.org/euclid.tbilisi/1528769063


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References

  • A. Banerjee, On the uniqueness of meromorphic functions that share two sets, Georgian Math., 15 (1) (2008), 21-38.
  • A. Banerjee, Bi-unique range sets for meromorphic functions, Nihonkai Math. J., 24(2) (2013), 121-134.
  • A. Banerjee and P. Bhattacharajee, Uniqueness of derivatives of meromorphic function sharing two or three sets, Turkish J. Math., 34(1) (2010), 21-34.
  • A. Banerjee and P. Bhattacharajee, Uniqueness and set sharing of derivatives of meromorphic functions, Math. Slovaca, 61(2) (2010), 197-214.
  • A. Banerjee and S. Mallick, Uniqueness of meromorphic functions sharing two finite sets in $\mathbb{C}$ with finite weight II, Rend. Circ. Mat. Palermo., DOI 10.1007/s12215-015-0208-8.
  • M. Fang and H. Guo, On meromorphic functions sharing two values, Analysis 17 (1997), 355-366.
  • F. Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976); Lecture Notes in Math., 599 (1977), 51-69, Springer(Berlin).
  • W. K. Hayman, Meromorphic functions, The Clarendon Press, Oxford (1964).
  • I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28(2) (2001), 83-91.
  • I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-206.
  • I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46 (2001), 241-253.
  • I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38 (2002), 119-128.
  • I. Lahiri and A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44 (2004), 575-584.
  • P. Li and C. C. Yang, On the unique range set for meromorphic functions, Proc. Amer. Math. Soc., 124 (1996), 177-185.
  • A. Z. Mokhon'ko, On the Nevanlinna characteristics of some meromorphic functions, in "Theory of functions, functional analysis and their applications", Izd-vo Khar'kovsk, Un-ta, 14 (1971), 83-87.
  • B. Yi and Y. H. Li, The uniqueness of meromorphic functions that share two sets with CM, Acta Math. Sinica Chinese Ser., 55(2) (2012), 363-368.
  • H. X. Yi, Uniqueness of meromorphic functions and a question of Gross, Sci. China (A), 37(7) (1994), 802-813.
  • H. X. Yi, Meromorphic functions that share two sets, Acta Math Sinica, 45 (2002), 75-82
  • H. X. Yi and W. C. Lin, Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J., 46 (2006), 437-444.