The norm of pre-Schwarzian derivatives on bi-univalent functions of order \(\alpha\). (English) Zbl 1405.30014
Summary: In the present investigation, we give the best estimates for the norm of the pre-Schwarzian derivative \( T_{f}(z)=\frac{f''(z)}{f'(z)} \) for bi-starlike functions and a new subclass of bi-univalent functions of order \(\alpha\), where \(\|T_f\|=\sup_{|z|<1}(1-|z|^2)|\frac{f''(z)}{f'(z)}|\).
MSC:
| 30C45 | Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) |
| 30C50 | Coefficient problems for univalent and multivalent functions of one complex variable |
