%0 Journal Article %T The norm of pre-Schwarzian derivatives on bi-univalent functions of order $\alpha$ %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A Rahmatan, H. %A Najafzadeh, Sh. %A Ebadian, A. %D 2017 %\ 10/01/2017 %V 43 %N 5 %P 1037-1043 %! The norm of pre-Schwarzian derivatives on bi-univalent functions of order $\alpha$ %K Bi-Univalent Functions %K bi-starlike functions %K subordina- tion %K pre-Schwarzian derivatives %R %X ‎In the present investigation‎, ‎we give the best estimates for the norm of the pre-Schwarzian derivative $ T_{f}(z)=\dfrac{f^{''}(z)}{f^{'}(z)} $ for bi-starlike functions and a new subclass of bi-univalent functions of order $ \alpha $‎, ‎where‎ ‎$\Vert T_{f} \Vert= \sup_{|z|<1} (1-|z|^{2})|\dfrac{f^{''}(z)}{f^{'}(z)}|$. %U http://bims.iranjournals.ir/article_976_ceb99544ec2644d892bcda3f82707ac5.pdf