International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 177-183

On a subclass of α-convex λ-spiral functions

F. M. Al-Oboudi1 and M. M. Hidan2

1Department of Mathematics, Girl's College of Education, Science Sections, Sitteen Street, Malaz, Riyadh, Saudi Arabia
2Department of Mathematics, Girl's College of Education, Science Sections, Kabel, Abha, Saudi Arabia

Received 21 November 2000; Revised 22 February 2001

Copyright © 2002 F. M. Al-Oboudi and M. M. Hidan. 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 H denote the class of functions f(z)=z+k=2akzk which are analytic in the unit disc Δ={z:|z|<1}. In this paper, we introduce the class Mαλ[A,B] of functions fH with f(z)f(z)/z0, satisfying for zΔ:{(eiλαcosλ)(zf(z)/f(z))+αcosλ(1+zf(z)/f(z))}cosλ((1+Az)/(1+Bz))+isinλ, where denotes subordination, α and λ are real numbers, |λ|<π/2 and 1B<A1. Functions in Mαλ[A,B] are shown to be λ-spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.