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The Journal of Analysis

, Volume 26, Issue 1, pp 119–134 | Cite as

Some further studies on the uniqueness of meromorphic functions sharing three sets

  • Arindam Sarkar
Original Research Paper
  • 38 Downloads

Abstract

In this paper we improve and rectify two recent results of Banerjee and Majumder (Analysis 34(2):143–162, 2014) relating to the uniqueness of meromorphic functions sharing three sets. We also show that the uniqueness of two nonconstant meromorphic functions can be achieved without any condition on deficiency when at least one of the functions under consideration assumes a certain value.

Keywords

Meromorphic function Uniqueness Set sharing 

Mathematics Subject Classification

30D35 

Notes

Compliance with ethical standards

Conflict of interest

We have no potential conflict of interest.

References

  1. 1.
    Banerjee, A. 2007. On a question of Gross. Journal of Mathematical Analysis and Applications 327 (2): 1273–1283.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Banerjee, A. 2007. Some uniqueness results on meromorphic functions sharing three sets. Annales Polonici Mathematici 92 (3): 261–274.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Banerjee, A. 2009. Uniqueness of meromorphic functions that share three sets. Kyungpook Mathematical Journal 49: 15–29.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Banerjee, A. 2010. On the uniqueness of meromorphic functions sharing two sets. Communications in Mathematical Analysis 10 (10): 1–10.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Banerjee, A., and S. Majumder. 2014. Uniqueness of meromorphic functions sharing three sets—Further study. Analysis 34 (2): 143–162.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Fang, M., and W. Xu. 1997. A note on a problem of Gross. Chinese Journal of Contemporary Mathematics 18 (4): 395–402.MathSciNetGoogle Scholar
  7. 7.
    Gross, F., 1977. Factorization of meromorphic functions and some open problems. In Proceedings conference University of Kentucky. Lecture notes in mathematics, Vol. 599, 51–69. Berlin: Springer.Google Scholar
  8. 8.
    Groos, F., and C.C. Yang. 1982. On preimage range sets of meromorphic functions. Proceedings of the Japan Academy 58: 17–20.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hayman, W.K. 1964. Meromorphic functions. Oxford: Clarendon Press.zbMATHGoogle Scholar
  10. 10.
    Lahiri, I. 2001. Weighted sharing and uniqueness of meromorphic functions. Nagoya Mathematical Journal 161: 193–206.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lahiri, I. 2001. Weighted value sharing and uniqueness of meromorphic functions. Complex Variables: Theory and Applications 46: 241–253.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Lahiri, I. 2002. On a question of Hong Xun Yi. Archives of Mathematics (Brno) 38: 119–128.MathSciNetzbMATHGoogle Scholar
  13. 13.
    Lin, W.C., and H.X. Yi. 2003. Uniqueness theorem for meromorphic functions that share three sets. Complex Variables: Theory and Applications 48 (4): 315–327.MathSciNetzbMATHGoogle Scholar
  14. 14.
    Mohon’ko, A.Z. 1971. On the Nevanlinna Characteristics of some meromorphic functions. Theory of Functions, Functional Analysis and Their Applications 14: 83–87.MathSciNetGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsKandi Raj CollegeKandiIndia

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