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SOME RESULTS ON THE QUESTIONS OF KIT-WING YU

  • Majumder, Sujoy
  • Received : 2015.05.14
  • Published : 2016.04.30

Abstract

The paper deals with the problem of meromorphic functions sharing a small function with its differential polynomials and improves the results of Liu and Gu [9], Lahiri and Sarkar [8], Zhang [13] and Zhang and Yang [14] and also answer some open questions posed by Kit-Wing Yu [16]. In this paper we provide some examples to show that the conditions in our results are the best possible.

Keywords

uniqueness;meromorphic function;sharing small function

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. G. G. Gundersen, Meromorphic functions that share finite values with their derivative, J. Math. Anal. Appl. 75 (1980), no. 2, 441-446. https://doi.org/10.1016/0022-247X(80)90092-X
  3. G. G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), no. 2, 299-309. https://doi.org/10.2140/pjm.1983.105.299
  4. G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), no. 1, 88-95. https://doi.org/10.1006/jmaa.1998.5959
  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 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
  8. I. Lahiri and A. Sarkar, Uniqueness of a meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Art. 20, 9 pp.
  9. L. Liu and Y. Gu, Uniqueness of meromorphic functions that share one small function with their derivatives, Kodai Math. J. 27 (2004), no. 3, 272-279. https://doi.org/10.2996/kmj/1104247351
  10. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  11. E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206. https://doi.org/10.1007/BF01303627
  12. L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Lecture Notes in Math., Vol. 599, pp. 101-103, Springer-Verlag, New York, 1977.
  13. Q. C. Zhang, Meromorphic function that share one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Art. 116, 13 pp.
  14. J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck concerning meromorphic functions sharing one small function with their derivatives, Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 1, 141-149.
  15. C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112. https://doi.org/10.1007/BF01110921
  16. K. W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 21, 7 pp.