International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2002 / Article

Open Access

Volume 30 |Article ID 943130 | 7 pages |

On a subclass of α-convex λ-spiral functions

Received21 Nov 2000
Revised22 Feb 2001


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.

Copyright © 2002 Hindawi Publishing Corporation. 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.

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