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

## TL;DR

This paper corrects previous inaccuracies in estimating the norm of the pre-Schwarzian derivative for bi-starlike functions of order alpha, providing accurate proofs and bounds.

## Contribution

It offers corrected proofs and bounds for the norm of the pre-Schwarzian derivative on bi-starlike functions of order alpha, improving upon prior work.

## Key findings

- Corrected bounds for the pre-Schwarzian norm
- Valid proofs for bi-starlike functions of order alpha
- Clarification of previous inaccuracies

## Abstract

In the present paper we estimate the norm of the pre-Schwarzian derivative of bi-starlike functions of order $\alpha$ where $\alpha\in[0,1)$. Initially this problem 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.