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NORMAL FAMILY OF MEROMORPHIC FUNCTIONS

  • Wang, Jian-Ping (Department of Mathematics Shaoxing College of Arts and Sciences)
  • Received : 2013.02.19
  • Published : 2014.05.31

Abstract

We study normality for families of meromorphic functions which is related to an extended version of a Hayman's conjecture on value distribution, and prove several normality criteria for meromorphic functions and certain non-homogeneous differential polynomials.

Keywords

References

  1. A. Alotaibi, On the zeros of $af(f^{(k)})^n$ - 1 for $n{\geq}2$, Comput. Methods Funct. Theory 4 (2004), no. 1, 227-235. https://doi.org/10.1007/BF03321066
  2. W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), no. 2, 355-373.
  3. M. Buck, A theorem on homogeneous differential polynomials, Results Math. Online First; DOI 10.1007/s00025-012-0234-1(2012).
  4. H. H. Chen and M. L. Fang, On the value distribution of $f^nf^{\prim}$, Sci. China, Ser. A. 38 (1995), 789-798.
  5. J. Clunie, On a result of Hayman, J. London Math. Soc. 42 (1967), 389-392.
  6. W. Doeringer, Exceptional values of differetial polynomials, Pacific J. Math. 98 (1982), no. 1, 55-62. https://doi.org/10.2140/pjm.1982.98.55
  7. W. K. Hayman, Research Problems in Function Theory, Athlone Press, London, 1967.
  8. X. J. Huang and Y. X. Gu, On the value distribution of $f^2f^{(k)}$, J. Aust. Math. Soc. 78 (2005), no. 1, 17-26. https://doi.org/10.1017/S1446788700015536
  9. J. K. Langley, The zeros of $ff^{{\prime}{\prime}}$ - b, Results Math. 44 (2003), no. 1-2, 130-140. https://doi.org/10.1007/BF03322919
  10. E. Mues, Uber ein problem von Hayman, Math. Z. 164 (1979), no. 3, 239-259. https://doi.org/10.1007/BF01182271
  11. X. C. Pang and L. Zalcman, On theorems of Hayman and Clunie, New Zealand J. Math. 28 (1999), no. 1, 71-75.
  12. J. L. Schiff, Normal Families, Springer, New York, Berlin, Heidelberg, 1993.
  13. J. P. Wang, On the zeros of $f^n(z)f^{(k)}(z)-c(z)$, Complex Var. Elliptic Equ. 48 (2003), no. 8, 695-703. https://doi.org/10.1080/0278107031000152607
  14. C. C. Yang and P. C. Hu, On the value distribution of $ff^{(k)}$, Kodai Math. J. 19 (1996), no. 2, 157-167. https://doi.org/10.2996/kmj/1138043595
  15. C. C. Yang, L. Yang, and Y. F. Wang, On the zeros of $f(f^{(k)})^n-{\alpha}$, Chin. Sci. Bull. 38 (1993), no. 24, 2125-2128.
  16. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Dordrecht, Beijing, New York, Kluwer Academic Publishers and Science Press, 2003.
  17. L. Zalcman, Normal families: New perspectives, Bull. Amer.Math. Soc. (N.S.) 35 (1998), no. 3, 215-230. https://doi.org/10.1090/S0273-0979-98-00755-1
  18. C. P. Zeng, Normality and shared values with multiple zeros, J. Math. Anal. Appl. 394 (2012), no. 2, 683-686. https://doi.org/10.1016/j.jmaa.2012.05.020