International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 12, Pages 855-857
doi:10.1155/S0161171200001824
On a class of univalent functions
3A/95 Azad Nagar, Kanpur 208002, India
Received 3 March 1998
Copyright © 2000 Vikramaditya Singh. 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
We consider the class of univalent functions
f(z)=z+a3z3+a4z4+⋯ analytic in the unit disc and
satisfying |(z2f′(z)/f2(z))−1|<1, and show that such functions are starlike if they satisfy
|(z2f′(z)/f2(z))−1|<(1/2).