DOI QR코드

DOI QR Code

Uniqueness of Certain Non-Linear Differential Polynomials Sharing 1-Points

  • Received : 2009.08.18
  • Accepted : 2010.12.24
  • Published : 2011.03.31

Abstract

Using the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain non-linear differential polynomials share the same 1-points. Though the main concern of the paper is to improve a result of Fang [5] but as a consequence of the main result we improve and supplement some former results of Lahiri-Sarkar [16], Fang-Fang[6] et. al.

Keywords

References

  1. T. C. Alzahary and H. X. Yi, Weighted value sharing and a question of I. Lahiri, Complex Var. Theory Appl., 49(15)(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. A. Banerjee, On uniqueness for non-linear differential polynomials sharing the same 1-points, Ann. Polon. Math., 89(3)(2006), 259-272. https://doi.org/10.4064/ap89-3-3
  4. A. Banerjee, A uniqueness result on some differential polynomials sharing 1 points, Hiroshima Math. J., 37(3)2007, 397-408.
  5. M. L. Fang, Uniqueness and value sharing of entire functions, Comput. Math. Appl., 44(2002), 823-831. https://doi.org/10.1016/S0898-1221(02)00194-3
  6. C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44(2002), 607-617. https://doi.org/10.1016/S0898-1221(02)00175-X
  7. M. L. Fang and W. Hong, A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math., 32(9)(2001), 1343-1348.
  8. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  9. I. Lahiri, Uniqueness of meromorphic functions when two linear differential polynomials share the same 1-points, Ann. Polon. Math., 71(2)(1999), 113-128. https://doi.org/10.4064/ap-71-2-113-128
  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, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253. https://doi.org/10.1080/17476930108815411
  12. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.
  13. I. Lahiri and N. Mandal, Uniqueness of nonlinear differential polynomials sharing simple and double 1-points, Int. J. Math. Math. Sci., 12(2005), 1933-1942.
  14. I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc., 43(1)(2006), 161-168. https://doi.org/10.4134/BKMS.2006.43.1.161
  15. I. Lahiri and A. Sarkar, Uniqueness of a meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5(1)(2004), Art. 20.
  16. I. Lahiri and A. Sarkar, Nonlinear differential polynomials sharing 1-points with weight two, Chinese J. Contemp. Math., 25(3)(2004), 325-334.
  17. I. Lahiri and P. Sahoo, Uniqueness of non-linear differential polynomials sharing 1-points, Georgian Math. J., 12(1)(2005), 131-138.
  18. W. C. Lin, Uniqueness of differential polynomials and a problem of Lahiri, Pure Appl. Math., 17(2)(2001), 104-110 (in Chinese).
  19. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math., 35(2)(2004), 121-132.
  20. H. Qiu and M. Fang, On the uniqueness of entire functions, Bull. Korean Math. Soc., 41(1)(2004), 109-116. https://doi.org/10.4134/BKMS.2004.41.1.109
  21. C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125(1972), 107-112. https://doi.org/10.1007/BF01110921
  22. H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
  23. Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [Online http://jipam.vu.edu.au/].

Cited by

  1. Meromorphic functions whose certain differential polynomials share a small function with finite weight vol.33, pp.2, 2013, https://doi.org/10.1524/anly.2013.1185
  2. Certain Nonlinear Differential Polynomials Sharing a Nonzero Polynomial with Finite Weight vol.55, pp.3, 2015, https://doi.org/10.5666/KMJ.2015.55.3.653