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STUDY OF BRÜCK CONJECTURE AND UNIQUENESS OF RATIONAL FUNCTION AND DIFFERENTIAL POLYNOMIAL OF A MEROMORPHIC FUNCTION

  • 투고 : 2022.02.03
  • 심사 : 2022.04.02
  • 발행 : 2022.06.30

초록

Let f be a non-constant meromorphic function in the open complex plane ℂ. In this paper we prove under certain essential conditions that R(f) and P[f], rational function and differential polynomial of f respectively, share a small function of f and obtain a conclusion related to Brück conjecture. We give some examples in support to our result.

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참고문헌

  1. S. Bhoosnurmath and S. R. Kabbur, On entire and meromorphic functions that share one small function with their differential polynomial, Hindawi Publishing Corporation, Int. J. Analysis 2013, Article ID 926340.
  2. A. Banerjee and B. Chakraborty, Further investigations on a questions of Zhang and Lu, Ann. Univ. Paedagog. Crac. Stud. Math, 14 (2015), 105-119. https://doi.org/10.1515/aupcsm-2015-0008
  3. A. Banerjee and B. Chakraborty, On the generalizations of Bruck conjecture, Commun. Korean Math. Soc., 32 (2016), 311-327.
  4. A. Chen and G. Zhang, Unicity of meromorphic function and its derivative, Kyungpook. Math. J, 50 (2010), 71-80. https://doi.org/10.5666/KMJ.2010.50.1.071
  5. K. S. Charak and B. Lal, Uniqueness of p(f) and P[f], Turk J Math. 40 (2016), 569-581. https://doi.org/10.3906/mat-1503-85
  6. B. Chakraborty, Some uniqueness results related to the bruck conjecture, Analysis, 38(2) 2018, 91-100. https://doi.org/10.1515/anly-2017-0060
  7. B. Chakraborty, Uniqueness of power of a meromorphic function with its differential polynomial, Tamkang. J. Math., 50 (2019), 133-147. https://doi.org/10.5556/j.tkjm.50.2019.2673
  8. Hayman, W. K., Meromorphic function, Clarendon Press, Oxford, (1964).
  9. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241-253.
  10. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. https://doi.org/10.1017/S0027763000027215
  11. I. Lahiri, Uniqueness of meromorphic functions and its derivatives, J. Inequal. Pure. Appl. Math. 5 (2004), Art. 20.
  12. N. Li, and L. Z. Yang, Meromorphic function that shares one small functions with its differential polynomial, Kyunpook Math. J. 50 (2010), 447-454. https://doi.org/10.5666/KMJ.2010.50.3.447
  13. N. Li, L. Yang and K. Liu, A further result related to a conjecture of R. Bruck, Kyungpook. Math. J, 56 (2016), 451-464. https://doi.org/10.5666/KMJ.2016.56.2.451
  14. A. Z. Mohon's ko, On the Nevanlinna characterstics of some meromorphic functions, Theory of Functions. Functional Analysis and Their Applications 14 (1971), 83-87.
  15. L. Yang, Value distributions theory, Springer-Verlag, Berlin, (1993).
  16. H. X. Yi and C. C. Yang, Uniqueness theory of meromorphic functions(in Chinese), Science Press, Beijing, (1995).
  17. J. L. Zhang and L. Z. Yang, Some result related to a conjecture of Bruck, J. Inequal. Pure. Appl. Math. 8 (2007), Art. 18.