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  • Research Article
  • Open Access

Subordination and Superordination on Schwarzian Derivatives

Journal of Inequalities and Applications20082008:712328

  • Received: 4 September 2008
  • Accepted: 30 October 2008
  • Published:


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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Authors’ Affiliations

School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Penang, Malaysia
Department of Mathematics, University of Delhi, Delhi, 110 007, India
Department of Mathematics, Rajah Serfoji Government College, Thanjavur, 613 005, India


© Rosihan M. Ali et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.