International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 321-330
On close-to-convex functions of complex order
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403, OH, USA
Received 15 November 1988
Copyright © 1990 H. S. Al-Amiri and Thotage S. Fernando. 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.
The class of starlike functions of complex order was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class of functions close-to-convex of complex order , and its generalization, the classes where is a nonnegative integer. Here . Sharp coefficient bounds are determined for as well as several sufficient conditions for functions to belong to . The authors also obtain some distortion and covering theorems for and determine the radius of the largest disk in which every belongs to . All results are sharp.