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Journal of Mathematics
Volume 2013, Article ID 930290, 4 pages
Research Article

Sufficient Conditions and Applications for Carathéodory Functions

School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 27 November 2012; Accepted 19 December 2012

Academic Editor: Jen-Chih Yao

Copyright © 2013 Neng Xu. 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.


Let be the class of functions of the form which are analytic in . By using the method of differential subordinations, we give some sufficient conditions for Carathéodory function, that is, if satisfies and where , , , , , then . Some useful consequences of this result are also given.