On Drygas functional equation on groups

Drygas (1987) introduced the functional equation f(xy) + f(xy(-1)) = 2f(x) + f(y) + f(y(-1)) in connection with the characterization of quasi-inner-product spaces. In this paper, we study 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. On groups, this system generalizes the functional equation introduced by Drygas.