International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 17, Pages 2841-2846
doi:10.1155/IJMMS.2005.2841
On a subclass of n-starlike functions
1Department of Mathematics, “Lucian Blaga” University of Sibiu, 5–7 Ion Raṭiu Street, Sibiu 550012, Romania
2Department of Mathematics, School of Science and Engineering, Kinki University, Higashiosaka, Osaka 577-8502, Japan
Received 21 February 2005
Copyright © 2005 Mugur Acu and Shigeyoshi Owa. 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.
Abstract
In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized with f(w)=f'(w)−1=0 and w a fixed point in U. In 2005, the authors introduced the classes of functions close to convex and α-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that for w=0, the well-known classes of starlike, convex, close-to-convex, and α-convex functions are obtained. In this paper, we continue the investigation of the univalent functions normalized with f(w)=f'(w)−1=0 and w, where w is a fixed point in U.