Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 10 (2015), 95 -- 111

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ON THE BI UNIQUE RANGE SETS FOR DERIVATIVES OF MEROMORPHIC FUNCTIONS

Abhijit Banerjee and Sanjay Mallick

Abstract. In the paper we introduce the notion of Bi Unique Range Sets for derivatives of meromorphic functions and with the aid of the same we improve all previous results regarding derivatives of set sharing.

2010 Mathematics Subject Classification: 30D35.
Keywords: Meromorphic function; Uniqueness; Shared Set; Weighted sharing.

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References

  1. A. Banerjee, On the uniqueness of meromorphic functions that share two sets, Georgian Math., 15 (1) (2008), 21-38. MR2418873(2009d:30067). Zbl 1159.30018.

  2. A. Banerjee, Uniqueness of meromorphic functions sharing two sets with finite weight, Portugal. Math., (N.S.) 65(1) (2008), 81-93. MR2387089(2009a:30065). Zbl 1146.30014.

  3. A. Banerjee, Some further results on a question of Yi, Publ. De Inst. Math., 92(106)(2012), 177-187. MR3051644(Reviewed). Zbl 1289.30176.

  4. A. Banerjee and P. Bhattacharajee, Uniqueness of Derivatives Of Meromorphic Function Sharing Two Or Three Sets, Turkish J. Math., 34(1) (2010), 21-34. MR2654413(2011e:30084). Zbl 1189.30064.

  5. A. Banerjee and P. Bhattacharajee, Uniqueness and set sharing of derivatives of meromorphic functions, Math. Slovaca, 61(2) (2010), 197-214. MR2786694(2012d:30078). Zbl 1265.30141.

  6. M.Fang and H.Guo, On meromorphic functions sharing two values, Analysis 17 (1997), 355-366. MR1600358(99b:30039). Zbl 0894.30020.

  7. M.Fang and I. Lahiri, Unique range set for certain meromorphic functions, Indian J. Math., 45(2)(2003), 141-150. MR2035902(2004k:30063). Zbl 1048.30014.

  8. F. Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976); Lecture Notes in Math., 599(1977), pp.51-69, Springer(Berlin). MR0450529(56:8823). Zbl 0357.30007.

  9. F. Gross and C. C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad., 58 (1982), 17-20. MR0649056(83d:30027). Zbl 0501.30026.

  10. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964). MR0164038(29:1337). Zbl 0115.06203.

  11. I. Lahiri, The range set of meromorphic derivatives, Northeast Math. J., 14(3) (1998), 353-360. MR1685269(2000b:30040). Zbl 0934.30027.

  12. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci., 28(2)(2001), 83-91. MR1885054(2002k:30053). Zbl 0999.30023.

  13. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206. MR1820218(2001m:30034). Zbl 0981.30023.

  14. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001),241-253. MR1869738(2002h:30033). Zbl 1025.30027.

  15. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128. MR1909593(2003c:30031). Zbl 1087.30028.

  16. I. Lahiri and A.Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44(2004), 575-584. MR2108462. Zbl 1070.30015.

  17. W. C. Lin and H. X. Yi, Some further results on meromorphic functions that share two sets, Kyungpook Math. J., 43 (2003), 73-85. MR1961610(2004k:30068). Zbl 1064.30023.

  18. 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.

  19. H.Y. Xu, C. F. Yi, T.B. Cao, Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight, Ann. Polon. Math., 95 (2009), 55-66. MR2466013(2010a:30053). Zbl 1169.30010.

  20. H.Y. Xu, T.B. Cao and S. Liu, Uniqueness results of meromorphic functions whose nonlinear differential polynomials have one nonzero pseudo value, Math. Vesnik, 64(1)(2012), 1-16. MR2843146(2012k:30093). Zbl 1289.30195.

  21. H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J., 22 (1999), 264-272. MR1700596(2001d:30054). Zbl 0939.30020.

  22. H. X. Yi, Unicity theorems for meromorphic or entire functions II, Bull. Austral. Math. Soc., 52(1995) 215-224. MR1348480(96i:30024). Zbl 0844.30022.

  23. H. X. Yi and W. C. Lin, Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J., 46 (2006), 437-444. MR2261398(2007h:30033). Zbl 1110.30017.

  24. H. X. Yi and W. R. Lü, Meromorphic functions that share two sets II, Acta Math. Sci. Ser.B Engl. Ed., 24(1)(2004), 83-90. MR2036066(2005a:30059). Zbl 1140.30315.




Abhijit Banerjee Sanjay Mallick
Department of Mathematics, Department of Mathematics,
University of Kalyani, University of Kalyani,
West Bengal, 741235, India. West Bengal, 741235, India.
E-mail: abanerjee_kal@yahoo.co.in E-mail: sanjay.mallick1986@gmail.com
          abanerjeekal@gmail.com           smallick.ku@gmail.com





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