International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 39840, 12 pages
doi:10.1155/IJMMS/2006/39840

Subclasses of α-spirallike functions associated with Ruscheweyh derivatives

Neng Xu1 and Dinggong Yang2

1Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China
2Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, China

Received 9 May 2005; Revised 25 September 2005; Accepted 20 October 2005

Copyright © 2006 Neng Xu and Dinggong Yang. 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

Making use of the Ruscheweyh derivatives, we introduce the subclasses T(n,α,λ)(n∈{0,1,2,3,…},−π/2<α<π/2,and0≤λ≤cos2α) of functions f(z)=z+∑k=2∞akzk which are analytic in |z|<1. Subordination and inclusion relations are obtained. The radius of α-spirallikeness of order ρ is calculated. A convolution property and a special member of T(n,α,λ) are also given.