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On Drygas functional equation on groups

Valeriĭ A. Faĭziev, Prasanna K. Sahoo


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−1x) = 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.


Additive character of a group, bihomomorphism, Drygas functional equation, free group, homomorphism, Jensen functional equation, n-Abelian group, and quadratic functional equation.

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