Copyright © 2010 Soon-Mo Jung and Janusz Brzdęk. 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 investigate the approximate solutions
of the delay differential equation
with an initial condition, where
are real constants. We show that they can be “approximated” by solutions of the equation that are constant on the interval
and, therefore, have quite simple forms. Our results correspond to the notion of stability introduced by Ulam and Hyers.