International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 281-288

The second coefficient of a function with all derivatives univalent

A. Sathaye and S. M. Shah

Department of Mathematics, University of Kentucky, Lexington 40506, Kentucky, USA

Received 7 July 1981; Revised 9 December 1981

Copyright © 1982 A. Sathaye and S. M. Shah. 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.


We consider the second coefficient of a class of functions, univalent and normalized, and with all derivatives univalent in the unit disk D, and improve on a known result. It is also shown that this bound is in a sense best possible.