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In the present paper we estimate the norm of the pre-Schwarzian derivative ofbi-starlike functions of order $\alpha$ where $\alpha\in[0,1)$. Initially thisproblem was handled by Rahmatan et al. in [Bull Iran Math Soc {\bf43}:1037-1043, 2017]. We pointed out that the proofs and bounds by Rahmatan et al.are incorrect and present correct proofs and bounds.

Notes on the norm of pre-Schwarzian derivatives on bi-univalent functions of order $\alpha$