DOI QR코드

DOI QR Code

UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH THEIR HOMOGENEOUS AND LINEAR DIFFERENTIAL POLYNOMIALS SHARING A SMALL FUNCTION

  • Lahiri, Indrajit (Department of Mathematics University of Kalyani) ;
  • Pal, Bipul (Department of Mathematics University of Kalyani)
  • Received : 2016.04.15
  • Published : 2017.05.31

Abstract

In this paper we study the uniqueness question of meromorphic functions whose certain differential polynomials share a small function.

Keywords

References

  1. A. Chen, X. Wang, and G. Zhang, Unicity of meromorphic function sharing one small function with its derivative, Int. J. Math. Math. Sci. 2010 (2010), Article Id 507454, 11 pages.
  2. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  3. J. D. Hinchliffe, On a result of Chuang related to Hayman's alternative, Comput. Methods Funct. Theory 2 (2002), no. 1, 293-297. https://doi.org/10.1007/BF03321023
  4. X. H. Hua, A unicity theorem for entire functions, Bull. London Math. Soc. 22 (1990), no. 5, 457-462. https://doi.org/10.1112/blms/22.5.457
  5. I. Lahiri, Uniqueness of meromorphic functions as governed by their differential polynomials, Yokohama Math. J. 44 (1997), no. 2, 147-156.
  6. I. Lahiri, Differential polynomials and uniqueness of meromorphic functions, Yokohama Math. J. 45 (1998), no. 1, 31-38.
  7. J. T. Li and P. Li, Uniqueness of entire functions concerning differential polynomials, Commun. Korean Math. Soc. 30 (2015), no. 2, 93-101. https://doi.org/10.4134/CKMS.2015.30.2.093
  8. E. Mues and M. Reinders, On a question of C. C. Yang, Complex Var. Theory Appl. 34 (1997), no. 1-2, 171-179. https://doi.org/10.1080/17476939708815045
  9. K. Shibazaki, Unicity theorems for entire functions of finite order, Mem. Nat, Defence Acad. (Japan) 21 (1981), no. 3, 67-71.
  10. C. C. Yang, On two entire functions which together with their first derivatives have the same zeros, J. Math. Anal. Appl. 56 (1976), no. 1, 1-6. https://doi.org/10.1016/0022-247X(76)90002-0
  11. C. C. Yang and H. X. Yi, A unicity theorem for meromorphic functions with deficient value, Acta Math. Sinica 37 (1994), no. 1, 62-72.
  12. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing and Kluwer Academic Publishers, New York, 2003.
  13. H. X. Yi, Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Var. Theory Appl. 14 (1990), no. 1-4, 169-176. https://doi.org/10.1080/17476939008814415
  14. H. X. Yi, A question of C. C. Yang on the uniqueness of entire functions, Kodai Math. J. 13 (1990), no. 1, 39-46. https://doi.org/10.2996/kmj/1138039158
  15. H. X. Yi, Unicity theorems for entire or meromorphic functions, Acta Math. Sin. (N.S.) 10 (1994), no. 2, 121-131. https://doi.org/10.1007/BF02580418
  16. H. X. Yi, Uniqueness theorems for meromorphic functions whose nth derivatives share the same 1-points, Complex Var. Theory Appl. 34 (1997), no. 4, 421-436. https://doi.org/10.1080/17476939708815064
  17. H. X. Yi and C. C. Yang, A uniqueness theorem for meromorphic functions whose nth derivatives share the same 1-points, J. Anal. Math. 62 (1994), 261-270. https://doi.org/10.1007/BF02835957