Subordination and Superordination on Schwarzian Derivatives
Let the functions q1 be analytic and let q2 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 f are obtained so that either q1(z)≺zf′(z)/f(...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/712328 |
| Summary: | Let the functions q1 be analytic and let q2 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 f are obtained so that either q1(z)≺zf′(z)/f(z)≺q2(z) or q1(z)≺1+zf′′(z)/f′(z)≺q2(z). As applications, sufficient conditions are determined relating the Schwarzian derivative to the starlikeness or convexity of f. |
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| ISSN: | 1025-5834 1029-242X |