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Subordination and Superordination on Schwarzian Derivatives

Abstract

Let the functions be analytic and let be analytic univalent in the unit disk. Using the methods of differential subordination and superordination, sufficient conditions involving the Schwarzian derivative of a normalized analytic function are obtained so that either or . As applications, sufficient conditions are determined relating the Schwarzian derivative to the starlikeness or convexity of .

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Correspondence to Rosihan M. Ali.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ali, R.M., Ravichandran, V. & Seenivasagan, N. Subordination and Superordination on Schwarzian Derivatives. J Inequal Appl 2008, 712328 (2008). https://doi.org/10.1155/2008/712328

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  • DOI: https://doi.org/10.1155/2008/712328

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  • Schwarzian Derivative