International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 1, Pages 125-132

On the definition of a close-to-convex function

A. W. Goodman and E. B. Saff

Mathematics Dept, University of South Florida, Tampa 33620, Florida, USA

Received 11 July 1977

Copyright © 1978 A. W. Goodman and E. B. Saff. 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.


The standard definition of a close-to-convex function involves a complex numerical factor eiβ which is on occasion erroneously replaced by 1. While it is known to experts in the field that this replacement cannot be made without essentially changing the class, explicit reasons for this fact seem to be lacking in the literature. Our purpose is to fill this gap, and in so doing we are lead to a new coefficient problem which is solved for n=2, but is open for n>2.