On the Hyers-Ulam-Rassias stability of the equation $f(x^2-y^2+rxy)=f(x^2)-f(y^2)+rf(xy)$

摘要

The following functional equation $$ f(x^{2}-y^{2}+rxy) = f(x^{2}) - f(y^{2}) + rf(xy) $$ can be considered as a variation of the Hossz'{u}'s functional equation. In this paper, the Hyers-Ulam-Rassias stability of the above functional equation shall be investigated.