# Notes on the norm of pre-Schwarzian derivatives of certain analytic functions

## TL;DR

This paper corrects previous proofs and establishes sharp bounds for the norm of pre-Schwarzian derivatives of specific analytic functions, enhancing understanding of their geometric properties.

## Contribution

It provides correct proofs and sharp bounds for the pre-Schwarzian derivative norm, correcting earlier inaccuracies in the literature.

## Key findings

- Corrected proofs for bounds on pre-Schwarzian derivatives
- Established sharp bounds for specific classes of analytic functions
- Clarified the geometric implications of these bounds

## Abstract

In this paper, we obtain sharp bounds for the norm of pre--Schwarzian derivatives of certain analytic functions. Initially this problem was handled by H. Rahmatan, Sh. Najafzadeh and A. Ebadian [Stud Univ Babe\c{s}--Bolyai Math {\bf61}(2): 155--162, 2016]. We pointed out that the proofs by Rahmatan et al. are incorrect and present correct proofs.