On uniqueness of two meromorphic functions when sharing three sets with finite weights
With the help of the notion of weighted sharing of sets, in this paper we have investigated on the question posed by Yi  regarding the uniqueness of meromorphic functions concerning three set sharing and obtained a result which significantly improved the recent results of Banerjee - Ahamed , Banerjee - Mukherjee  and Banerjee - Majumder  by removing the extra supposition as well as relaxing the nature of sharing. We have exhibited some examples to show the sharpness of the cardinalities of the set S 1 and the set S 2 considered in 1.1 and also to show that one can not obtained the same conclusions of the main results by considering any arbitrary sets.
Banerjee, A., Some uniqueness results on meromorphic functions sharing three sets, Ann. Polon. Math., 92(3)(2007), 261-274.
Banerjee, A., Uniqueness of meromorphic functions that share three sets, Kyungpook Math. J., 49(2009), 15-29.
Banerjee, A., Ahamed, M.B. On uniqueness of meromorphic functions sharing three sets with finite weights, Bull. Polish Acad. Sci., 62(3)(2014), 243–256.
Bnerjee, A., Majumder, S., Uniqueness of meromorphic functions sharing three sets - further study, Analysis, 34(2)(2014), 143–162.
Banerjee, A., Mukherjee, S., Uniqueness of meromorphic functions sharing two or three sets, Hokkaido Math. J., 37(2008), 507–530.
Fang, M.L., Uniqueness of admissible meromorphic functions in the unit disc, Sci. China (A), 42(4)(1999), 367–381.
Fang, M., Xu, W., A note on a problem of Gross, Chinese J. Contemporary Math., 18(4)(1997), 395-402.
Gross, F.; Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976); Complex Analysis, Lecture Notes in Math., 599(1977), 51–69, Springer Verlag.
Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford 1964.
Lahiri, I., Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206.
Lahiri, I., Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
Lahiri, I., Sarkar, A., Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5(1)(2004), Art.20 [ONLINE http://jipam.vu.edu.au/].
Lin, W.C., Yi, H.X., Uniqueness theorems for meromorphic functions that share three sets, Complex Var. Theory Appl., 48(2003), 315-327.
Mokhonko, A.Z., On the Nevanlinna characteristics of some meromorphic functions, Theo. Funct. Funct. Anal. Appl., Izd-vo Kharkovsk Un-ta, 14(1971), 83-87.
Qiu, H., Fang, M., A unicity theorem for meromorphic functions. Bull. Malaysian Math. Sci. Soc. 25(2002), 31-38.
Yi, H.X., On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119–133.
Yi, H.X., Uniqueness of meromorphic functions and a question of Gross, Science in China, 37(7)(A)(1994), 802–813.
Yi, H.X., Lin, W.C., Uniqueness theorems concerning a question of Gross, Proc. Japan Acad. Ser. A 80(2004), 136-140.
Zhang, Q.C., Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].
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