Abstract
The aim of the paper is to study the uniqueness problems of meromorphic functions when certain differential polynomials generated by them share a small function. With the aid of weighted sharing we prove four theorems first two of which improve the results due to Boussaf et al. (Indagationes Mathematicae 24:15–41, 2013) and last two improve a result due to Bhoosnurmath and Pujari (Bull Korean Math Soc 52:13–33, 2015).
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