International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 201-203
doi:10.1155/S0161171296000294
Univalence for convolutions
Department of Mathematics, University of Charleston, Charleston 29424, SC, USA
Received 10 May 1994
Copyright © 1996 Herb Silverman. 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
The radius of univalence is found for the convolution f∗g of functions f∈S (normalized univalent functions) and g∈C (close-to-convex functions). A lower bound for the radius of univalence is also determined when f and g range over all of S. Finally, a characterization of C provides an inclusion relationship.