Suppose that is a group. The system of functional equations
where is called stable if for any satisfying the system of inequalities
for some positive number , there is a solution of () and a positive number such that .
In this paper the authors prove that the system () is not stable on an arbitrary group, in general; the system is stable on Heisenberg group
where is a (commutative) field with characteristic different from two; the system is stable on certain class of -Abelian groups; and finally that any group can be embedded into a group, where the system () is stable. See also V. A. Fauiziev and P. K. Sahoo [Stability of Drygas functional equation on , Int. J. Appl. Math. Stat. 7, No. Fe07, 70–81 (2007)].