AIMS Mathematics, 2018, 3(4): 600-607. doi: 10.3934/Math.2018.4.600

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

1 School of Liberal Studies, Ambedkar University Delhi, 110006, Delhi
2 Department of Mathematics, AMITY School of Applied Science, AMITY University, 302003, Rajasthan

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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2. D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes¸-Bolyai Math., 31 (1986), 70–77.

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4. H. Rahmatan, Sh. Najafzadeh and A. Ebadian, The norm of pre-Schwarzian derivatives on biunivalent functions of order α, B. Iran. Math. Soc., 43 (2017), 1037–1043.

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© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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