DOI QR코드

DOI QR Code

Some Further Results on Weighted Sharing of Values for Meromorphic Functions Concerning a Result of Terglane

Li, Xiao-Min;Yi, Hong-Xun

  • Received : 2007.04.20
  • Published : 2008.09.30

Abstract

In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain some uniqueness theorems which improve those given by N. Terglane, Hong-Xun Yi & Xiao-Min Li, and others. Some examples are provided to show that the results in this paper are best possible.

Keywords

meromorphic functions;weighted sharing values;uniqueness theorems

References

  1. T. C. Alzahary and H. X. Yi, Weighted sharing three values and uniqueness of meromorphic functions, J. Math. Anal. Appl., 295(2004), 247-257. https://doi.org/10.1016/j.jmaa.2004.03.040
  2. G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc., 20 (1979), 457-566. https://doi.org/10.1112/jlms/s2-20.3.457
  3. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  4. X. M. Li and H. X. Yi, A note on a unicity theorem of N. Terglane, Complex Variables Theory Appl., 48 (2003), 111-118. https://doi.org/10.1080/0278107021000037147
  5. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-206.
  6. I. Lahiri, Weighted sharing of three values and uniqueness of meromorphic functions, Kodai Math. J., 24 (2001), 421-435. https://doi.org/10.2996/kmj/1106168813
  7. I. Lahiri and A. Sarkar, On a uniqueness theorem of Tohge, Arch. Math., 84(2005), 461-469. https://doi.org/10.1007/s00013-004-1217-6
  8. X. M. Li and H. X. Yi, Meromorphic functions sharing three values, J. Math. Soc. Japan, 56 (2004), 147-167. https://doi.org/10.2969/jmsj/1191418699
  9. A. Z. Mokhon'ko, On the Nevanlinna characteristics of some meromorphic functions, in: Theory of functions, functional analysis and their applications, Izd-vo Khar'kovsk. Un-ta, 14 (1971), 83-87.
  10. R. Nevanlinna, Le Thereme de Picard-Borel et La Theorie des Fonctions Meromorphes, Gauthier-Villars, Paris, 1929.
  11. N. Terglane, Identitatssatze in C meromorpher Funktionen als Ergebnis von Werteteilung, Diplomarbeit, RWTH Aachen, 1989.
  12. H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
  13. H. X. Yi and X. M. Li, On a result of Terglane concerning uniqueness of meromorphic functions, Indian J. pure appl. Math. 33(2002), 1785-1798.
  14. H. X. Yi, Meromorphic functions with weighted sharing of three values, Complex Variables Theory Appl., 50 (2005), 923-934. https://doi.org/10.1080/02781070500183060
  15. Q. C. Zhang, Meromorphic functions sharing three values, Indian J. Pure Appl. Math., 30 (1999), 667-682.