Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 384170, 8 pages
Research Article

Some Inclusion Relationships of Certain Subclasses of -Valent Functions Associated with a Family of Integral Operators

1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
2Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt
3Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt

Received 16 June 2013; Accepted 24 August 2013

Academic Editors: G. Gripenberg and B. Wang

Copyright © 2013 M. K. Aouf et al. 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.


By making use of the new integral operator , we introduce and investigate several new subclasses of -valent starlike, -valent convex, -valent close-to-convex, and -valent quasi-convex functions. In particular, we establish some inclusion relationships associated with the aforementioned integral operators. Some of the results established in this paper would provide extensions of those given in earlier works.