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Uniqueness Of Meromorphic Functions Sharing Two Sets With Finite Weight III
Last modified: 2013-12-06
Abstract
Lahiri [Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), pp.193-206.] introduced the denition of gradation of sharing known as weighted sharing of values and sets which measure how close a shared value is to being shared CM or to being shared IM.
With the notion of weighted sharing of sets this paper investigate the problem of uniqueness of meromorphic functions sharing two sets which improve and supplement some existing results of Lahiri [ On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.],
Banerjee [Uniqueness Of Meromorphic Functions Sharing Two Sets With Finite Weight, Portugal. Math. J., 65(1), 2008, 81-93.] and
yi and Lin [ Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J, 46 (2006), 437-444.]. We exhibit two examples to show that the condition over decient values which plays a key factor in the paper is the best possible.
With the notion of weighted sharing of sets this paper investigate the problem of uniqueness of meromorphic functions sharing two sets which improve and supplement some existing results of Lahiri [ On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.],
Banerjee [Uniqueness Of Meromorphic Functions Sharing Two Sets With Finite Weight, Portugal. Math. J., 65(1), 2008, 81-93.] and
yi and Lin [ Uniqueness of meromorphic functions and a question of Gross, Kyungpook Math. J, 46 (2006), 437-444.]. We exhibit two examples to show that the condition over decient values which plays a key factor in the paper is the best possible.
Keywords
Meromorphic functions, uniqueness, weighted sharing, shared set.