Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ON THE GENERALIZATIONS OF BRÜCK CONJECTURE

  • Received : 2015.07.04
  • Published : 2016.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain similar types of conclusions as that of $Br{\ddot{u}}ck$ [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover a number of examples have been exhibited to justify the necessity or sharpness of some conditions used in the paper. At last we pose an open problem for future research.

Keywords

Acknowledgement

Supported by : Department of Science and Technology, Govt.of India

References

  1. R. Bruck, On entire functions which share one value CM with their first derivative, Results Math. 30 (1996), no. 1-2, 21-24. https://doi.org/10.1007/BF03322176
  2. C. T. Chuang, On differential polynomials, Analysis of one complex variable (Laramie, Wyo., 1985) 12-32, World Sci. Publishing Singapore 1987.
  3. W. Doeringer, Exceptional values of differential polynomials, Pacific J. Math. 98 (1982), no. 1, 55-62. https://doi.org/10.2140/pjm.1982.98.55
  4. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  5. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206. https://doi.org/10.1017/S0027763000027215
  6. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), no. 3, 241-253. https://doi.org/10.1080/17476930108815411
  7. I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006) no. 1, 79-87.
  8. I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), no. 1, 95-100. https://doi.org/10.2996/kmj/1050496651
  9. I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Art.20.
  10. L. Liu, Uniqueness of meromorphic functions that share one small function with their derivatives, J. Math. Sci. Adv. Appl. 6 (2010), no. 2, 241-255.
  11. K. Liu and L. Z. Yang, Meromorphic functions that share one value with their derivatives, J. Inequal. Pure Appl. Math. 7 (2006), no. 3, Art. 93, 9 pp.
  12. K. Liu and L. Z. Yang, Meromorphic function that shares one small function with its differential polynomial, Kyungpook Math. J. 50 (2010), 447-454. https://doi.org/10.5666/KMJ.2010.50.3.447
  13. A. Z. Mohon'ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, functional analysis and their applications, Izd-vo Kha'kovsk, Unta 14 (1971), 83-87.
  14. E. Mues and N. Steinmetz, Meromorphe Funktionen die unit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206. https://doi.org/10.1007/BF01303627
  15. L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), pp. 101-103. Lecture Notes in Math., Vol. 599, Springer, Berlin, 1977.
  16. L. Z. Yang, Solution of a differential equation and its applications, Kodai Math. J. 22 (1999), no. 3, 458-464. https://doi.org/10.2996/kmj/1138044097
  17. H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (1991), no. 2, 119-133.
  18. Q. C. Zhang, The uniqueness of meromorphic functions with their derivatives, Kodai Math. J. 21 (1998), no. 2, 179-184. https://doi.org/10.2996/kmj/1138043871
  19. Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Art. 116, 13 pp.
  20. T. D. Zhang and W. R. Lu, Notes on meromorphic function sharing one small function with its derivative, Complex Var. Ellip. Eqn. 53 (2008), no. 9, 857-867. https://doi.org/10.1080/17476930802166386

Cited by

  1. Some uniqueness results related to the Brück conjecture vol.38, pp.2, 2018, https://doi.org/10.1515/anly-2017-0060