International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 3, Pages 177-183
doi:10.1155/S0161171202011110

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

Abstract

Let H denote the class of functions f(z)=z+∑k=2∞akzk which are analytic in the unit disc Δ={z:|z|<1}. In this paper, we introduce the class Mαλ[A,B] of functions f∈H with f(z)f′(z)/z≠0, satisfying for z∈Δ:{(eiλ−αcosλ)(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 −1≤B<A≤1. Functions in Mαλ[A,B] are shown to be λ-spiral like and hence univalent. Integral representation, coefficients bounds, and other results are given.