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UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS WITH REGARD TO MULTIPLICITY SHARING A SMALL FUNCTION

  • WAGHAMORE, HARINA P. (Department of Mathematics, Jnanabharathi Campus, Bangalore University) ;
  • ANAND, SANGEETHA (Department of Mathematics, Jnanabharathi Campus, Bangalore University)
  • Received : 2017.02.14
  • Accepted : 2017.06.21
  • Published : 2017.09.30

Abstract

In this paper, using the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain differential polynomials sharing a small function. The results obtained in this paper extend the theorem obtained by Jianren Long [9].

Keywords

References

  1. A. Banerjee, On uniqueness of meromorphic functions when two differential monomials share one value, Bull. Korean Math. Soc. 44 (2007), no. 4, 607-622. https://doi.org/10.4134/BKMS.2007.44.4.607
  2. A. Banerjee and S. Mukherjee, Uniqueness of meromorphic functions concerning differential monomials sharing the same value, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 50 (2007), no. 3, 191-206.
  3. S. S. Bhoosnurmath and S. R. Kabbur, Uniqueness and value sharing of meromorphic functions with regard to multiplicity, Tamkang J. Math. 44 (2013), no. 1, 11-22. https://doi.org/10.5556/j.tkjm.44.2013.840
  4. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
  5. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), no. 3, 241-253. https://doi.org/10.1080/17476930108815411
  6. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28 (2001), no. 2, 83-91. https://doi.org/10.1155/S0161171201011036
  7. S. Lin and W. Lin, Uniqueness of meromorphic functions concerning weakly weightedsharing, Kodai Math. J. 29 (2006), no. 2, 269-280. https://doi.org/10.2996/kmj/1151936441
  8. X. Lin and W. Lin, Uniqueness of entire functions sharing one value, Acta Math. Sci. Ser. B Engl. Ed. 31 (2011), no. 3, 1062-1076. https://doi.org/10.1016/S0252-9602(11)60298-1
  9. J. Long, Nonlinear differential polynomials of meromorphic functions with regard to multiplicity sharing a small function, J. Comput. Anal. Appl. 22 (2017), no. 7, 1220-10230.
  10. P. Sahoo and H. Karmakar, Results on uniqueness of entire functions whose certain difference polynomials share a small function, Anal. Math. 41 (2015) no. 4, 257-272. https://doi.org/10.1007/s10476-015-0302-3
  11. C. C. Yang, On deficiencies of differential polynomials. II, Math. Z. 125 (1972), 107-112. https://doi.org/10.1007/BF01110921
  12. C.-C. Yang and X. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), no. 2, 395-406.
  13. C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557, Kluwer Acad. Publ., Dordrecht, 2003.
  14. L. Yang, Value distribution theory, translated and revised from the 1982 Chinese original, Springer, Berlin, 1993.
  15. J.-L. Zhang and L.-Z. Yang, Some results related to a conjecture of R. Bruck, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 1, Article 18, 11 pp.
  16. X.-Y. Zhang, J.-F. Chen and W.-C. Lin, Entire or meromorphic functions sharing one value, Comput. Math. Appl. 56 (2008), no. 7, 1876-1883. https://doi.org/10.1016/j.camwa.2008.04.008