Subordination and Superordination on Schwarzian Derivatives

Rosihan M. Ali; V. Ravichandran; N. Seenivasagan

doi:10.1155/2008/712328

Research Article
Open Access

Subordination and Superordination on Schwarzian Derivatives

Rosihan M. Ali¹Email author,
V. Ravichandran² and
N. Seenivasagan³

Journal of Inequalities and Applications20082008:712328

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

Received: 4 September 2008
Accepted: 30 October 2008
Published: 10 November 2008

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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Schwarzian Derivative

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Authors’ Affiliations

(1)

School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800 Penang, Malaysia

(2)

Department of Mathematics, University of Delhi, Delhi, 110 007, India

(3)

Department of Mathematics, Rajah Serfoji Government College, Thanjavur, 613 005, India

Copyright

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.