@article { author = {Rahmatan, H. and Najafzadeh, Sh. and Ebadian, A.}, title = {The norm of pre-Schwarzian derivatives on bi-univalent functions of order $\alpha$}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {5}, pages = {1037-1043}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {‎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)}|$.}, keywords = {Bi-Univalent Functions,bi-starlike functions,subordina- tion,pre-Schwarzian derivatives}, url = {http://bims.iranjournals.ir/article_976.html}, eprint = {http://bims.iranjournals.ir/article_976_ceb99544ec2644d892bcda3f82707ac5.pdf} }