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

Document Type: Research Paper

Authors

Department of Mathematics‎, ‎Payame Noor University‎, ‎P.O‎. ‎Box 19395-3697 Tehran‎, ‎Iran.

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)}|$.

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Volume 43, Issue 5
September and October 2017
Pages 1037-1043
  • Receive Date: 13 June 2015
  • Revise Date: 27 March 2016
  • Accept Date: 31 March 2016