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WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS

  • Bhoosnurmath, Subhas S. (Department of Mathematics Karnatak University) ;
  • Pujari, Veena L. (Post Graduate Department of Mathematics Vijaya College)
  • Received : 2012.02.18
  • Published : 2015.01.31

Abstract

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

Keywords

References

  1. R. Dyavanal, Uniqueness and value-sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl. 374 (2011), no. 1, 335-345. https://doi.org/10.1016/j.jmaa.2010.09.002
  2. C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl. 44 (2002), no. 5-6, 607-617. https://doi.org/10.1016/S0898-1221(02)00175-X
  3. M. L. Fang and H. Guo, On meromorphic functions sharing two values, Analysis 17 (1997), no. 4, 355-366.
  4. M. L. Fang and X. H. Hua, Entire functions that share one value, J. Nanajing Univ. Math. Biquarterely 13 (1996), no. 1, 44-48.
  5. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), no. 3, 241-253. https://doi.org/10.1080/17476930108815411
  6. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic functions concerning fixed points, Complex Var. Theory Appl. 49 (2004), no. 11, 793-806.
  7. J. F. Xu and H. X. Yi, Uniqueness of entire functions and differential polynomials, Bull. Korean Math. Soc. 44 (2007), no. 4, 623-629. https://doi.org/10.4134/BKMS.2007.44.4.623
  8. L. Yang, Value Distribution Theory, Springer-Verlag, Berlin, 1993.
  9. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordredt, 2003.