The norm of pre-Schwarzian derivative on subclasses of bi-univalent functions

In the present paper, we give the best estimates for the norm of pre-Schwarzian derivatives $||{T_f}(z)|| = \mathop {\sup }\limits_{|z| < 1} (1 - |z{|^2})\left| {\frac{{f''(z)}}{{f'(z)}}} \right|$ for subclasses of bi-univalent functions.

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Bibliographic Details
Published inAIMS mathematics Vol. 3; no. 4; pp. 600 - 607
Main Authors Rana, Shalini, Goswami, Pranay, Shanker Dubey, Ravi
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2018
Subjects
bi-univalent functions| bi-starlike functions| subordination| pre-Schwarzian derivatives
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Summary:In the present paper, we give the best estimates for the norm of pre-Schwarzian derivatives $||{T_f}(z)|| = \mathop {\sup }\limits_{|z| < 1} (1 - |z{|^2})\left| {\frac{{f''(z)}}{{f'(z)}}} \right|$ for subclasses of bi-univalent functions.
ISSN:2473-6988
2473-6988
DOI:10.3934/Math.2018.4.600