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
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.
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.