ON THE STABILITY OF DRYGAS FUNCTIONAL EQUATION ON GROUPS

In this paper, we study the stability of the system of functional equations f(xy) + f(xy(-1)) = 2f(x) + f(y) + f(y(-1)) and f(yx) + f(y(-1)x) = 2f(x) + f(y) + f(y(-1)) on groups. Here f is a real-valued function that takes values on a group. Among others we proved the following results: 1) the system, in general, is not stable on an arbitrary group; 2) the system is stable on Heisenberg group UT(3, K), where K is a commutative field with characteristic different from two; 3) the system is stable on certain class of n-Abelian groups; 4) any group can be embedded into a group where this system is stable.