Uniqueness of P(f) and [P(f)]^(k) concerning weakly weighted sharing

2020/09/19 by Ahamed, Molla Basir
#30D35 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.09245

Abstract

In this paper, with the help of the idea of weakly weighted sharing introduced by Lin -Lin [Kodai Math. J., 29(2006), 269-280], we study the uniqueness of a polynomial expression P(f) and [P(f)]^(k) of a meromorphic function f sharing a small function. The main results significantly improved the result of Liu - Gu [Kodai Math. J., 27(3)(2004), 272-279]. This research work explores certain condition under which the polynomial P(f) can be reduced to a non-zero monomial, and as a consequence, the specific form of the function f is obtained. By some constructive examples it has been shown that some conditions in the main results can not be removed and some of the inequalities are sharp.

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