Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

On a Result of N. Terglane

  • Received : 2010.02.10
  • Accepted : 2011.01.20
  • Published : 2011.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.

Keywords

References

  1. T. C. Alzahary, Small functions of meromorphic functions sharing three values with finite weights, Indian J. Pure Appl. Math., 38(4)(2007), 305-316.
  2. G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc., 20(2)(1979), 457-466. https://doi.org/10.1112/jlms/s2-20.3.457
  3. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  4. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.
  5. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex. Var. Theory Appl., 46(3)(2001), 241-253. https://doi.org/10.1080/17476930108815411
  6. I. Lahiri, On a result of Ozawa concerning uniqueness of meromorphic functions II, J. Math. Anal. Appl., 283(1)(2003), 66-76. https://doi.org/10.1016/S0022-247X(03)00188-4
  7. I. Lahiri, Characteristic function of meromorphic functions sharing three values with finite weights, Complex Var. Theory Appl., 50(1)(2005), 69-78.
  8. I. Lahiri, Sharing three values with small weights, Hokkaido Math. J., 36(2007), 129- 142. https://doi.org/10.14492/hokmj/1285766655
  9. I. Lahiri, Weighted sharing of three values by meromorphic functions, Hokkaido Math. J., 37(2008), 41-58. https://doi.org/10.14492/hokmj/1253539586
  10. X. M. Li and H. X. Yi, A note on a unicity theorem of N. Terglane, Complex Var. Theory Appl., 48(2)(2003), 111-118. https://doi.org/10.1080/0278107021000037147
  11. N. Terglane, Identitatssatze in C meromorpher Funktionen als Ergebnis von Werteteilung, Diplomarbeit, RWTH Aachen, 1989.
  12. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
  13. Q. C. Zhang, A note on two results of Ueda and Mues, J. Math. Res., 31(1998), 451-454.