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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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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Abstract 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.
AbstractList 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.
Author Shanker Dubey, Ravi
Rana, Shalini
Goswami, Pranay
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CorporateAuthor 2 Department of Mathematics, AMITY School of Applied Science, AMITY University, 302003, Rajasthan
1 School of Liberal Studies, Ambedkar University Delhi, 110006, Delhi
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Snippet 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 -...
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SubjectTerms bi-univalent functions| bi-starlike functions| subordination| pre-Schwarzian derivatives
Title The norm of pre-Schwarzian derivative on subclasses of bi-univalent functions
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