Copyright © 2009 Takeshi Miura et al. 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.
Let be a set with a binary operation
such that, for each , either
or . We show the superstability of the functional equation
. More explicitly, if and
satisfies for each , then for all
, or for all . In the latter case, the constant is the best possible.