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International Journal of Mathematics and Mathematical Sciences
Volume 19, Issue 1, Pages 201-203
http://dx.doi.org/10.1155/S0161171296000294

Univalence for convolutions

Department of Mathematics, University of Charleston, Charleston 29424, SC, USA

Received 10 May 1994

Copyright © 1996 Hindawi Publishing Corporation. 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 fg of functions fS (normalized univalent functions) and gC (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.