International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 62925, 7 pages
doi:10.1155/2007/62925
Research Article

Sufficient Conditions for Janowski Starlikeness

Rosihan M. Ali, V. Ravichandran, and N. Seenivasagan

School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 USM, Malaysia

Received 10 March 2007; Revised 15 June 2007; Accepted 4 July 2007

Academic Editor: Teodor Bulboaca

Copyright © 2007 Rosihan M. Ali et al. 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 A,B,D,E∈[−1,1] and let p(z) be an analytic function defined on the open unit disk, p(0)=1. Conditions on A, B, D, and E are determined so that 1+βzp'(z) being subordinated to (1+Dz)/(1+Ez) implies that p(z) is subordinated to (1+Az)/(1+Bz). Similar results are obtained by considering the expressions 1+β(zp'(z)/p(z)) and 1+β(zp'(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.