International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 2, Pages 335-340
doi:10.1155/S0161171283000290

On the radius of univalence of convex combinations of analytic functions

Khalida I. Noor, Fatima M. Aloboudi, and Naeela Aldihan

 Mathematics Department, Science College of Education for Girls, Malaz, Sitteen Road, Riyadh, Saudi Arabia
Received 10 July 1982; Revised 21 February 1983

Abstract

We consider for α>0, the convex combinations f(z)=(1−α)F(z)+αzF′(z), where F belongs to different subclasses of univalent functions and find the radius for which f is in the same class.