On uniqueness of two meromorphic functions sharing three sets with finite weights
Abstract
With the help of the notion of weighted sharing of sets, this paper dealt with the question posed by Yi Yi-SC-1994 regarding the uniqueness of meromorphic functions concerning three set sharing. A result has been proved which significantly improved the recent results of Banerjee - Ahamed [Bull. Polish Acad. Sci., 62(3)(2014), 243--256.], \Banerjee - Mukherjee [Hokkaido Math. J., 37(2008), 507--530.] and Banerjee - Majumder [Analysis, 34(2)(2014), 143--162.] by relaxing the nature of sharing. Several examples have been exhibited to show the sharpness of the cardinalities of the sets S1 and S2 considered in Theorem 1.1. Moreover, we give some constructive examples to endorse the validity of our established theorem.
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