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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Keywords bi-univalent functions; bi-starlike functions; subordination; pre-Schwarzian derivatives

Citation: Shalini Rana, Pranay Goswami, Ravi Shanker Dubey. The norm of pre-Schwarzian derivative on subclasses of bi-univalent functions. AIMS Mathematics, 2018, 3(4): 600-607. doi: 10.3934/Math.2018.4.600

References

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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.
  • 5. T. S. Taha, Topics in Univalent Function Theory, Ph.D. Thesis, University of London, 1981.

 

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