International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 4, Pages 821-823

A note on Bazilevič functions

S. A. Halim and D. K. Thomas

Department of Mathematics and Computer Science, University of Swansea, Singleton Park, Swansea SA2 8PP, UK

Received 5 May 1989

Copyright © 1991 S. A. Halim and D. K. Thomas. 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.


For α>0, let B1(α) be the class of normalized analytic functions defined in the open unit disc D satisfying Re(f(z)/z)α1f(z)>0 for zD. The sharp lower bound for Re(f(z)/z)α is obtained and the result is generalized to some iterated integral operators.