DOI QR코드

DOI QR Code

Meromorphic Functions Sharing a Nonzero Polynomial IM

Sahoo, Pulak

  • Received : 2011.01.12
  • Accepted : 2012.07.24
  • Published : 2013.06.23

Abstract

We study the uniqueness of meromorphic functions concerning nonlinear differential polynomials sharing a nonzero polynomial IM. Though the main concern of the paper is to improve a recent result of the present author [12], as a consequence of the main result we also generalize two recent results of X. M. Li and L. Gao [11].

Keywords

Uniqueness;Meromorphic function;Nonlinear Differential Polynomials

References

  1. T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl., 49(2004), 1063-1078. https://doi.org/10.1080/02781070410001701074
  2. A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3587-3598.
  3. W. Bergweiler and X. C. Pang, On the derivative of meromorphic functions with multiple zeros, J. Math. Anal. Appl., 278(2003), 285-292. https://doi.org/10.1016/S0022-247X(02)00349-9
  4. M. L. Fang, A note on a problem of Hayman, Analysis (Munich), 20(2000), 45-49.
  5. M. L. Fang and H. L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl., 268(2002), 426-439. https://doi.org/10.1006/jmaa.2000.7270
  6. W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. of Math., 70(1959), 9-42. https://doi.org/10.2307/1969890
  7. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  8. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sc., 28(2001), 83-91. https://doi.org/10.1155/S0161171201011036
  9. I. Lahiri, On a question of Hong Xun Yi, Arch Math. (Brno), 38(2002), 119-128.
  10. X. M. Li and L. Gao, Meromorphic functions sharing a nonzero polynomial CM, Bull. Korean Math. Soc., 47(2010), 319-339. https://doi.org/10.4134/BKMS.2010.47.2.319
  11. P. Sahoo, Uniqueness of meromorphic functions when two differential polynomials share one value IM, Mat. Vesnik, 62(2010), 169-182.
  12. C. C. Yang and X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math., 22(1997), 395-406.
  13. L. Yang, Value Distribution Theory, Springer- Verlag, Berlin, 1993.
  14. H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
  15. Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6(2005), Art. 116.
  16. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253. https://doi.org/10.1080/17476930108815411
  17. C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125(1972), 107-112. https://doi.org/10.1007/BF01110921