科研之友
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摘要
We determine the general solution of the functional equation f(x + ky) + f(x - ky) = g(x + y) + g(x - y) + h(x) + h(y) for fixed integers k with k not equal 0, +/- 1 without assuming any regularity conditions for the unknown functions f, g, h, and (h) over tilde. The method used for solving these functional equations is elementary but it exploits an important result due to Hosszu. The solution of this functional equation can also be obtained in groups of certain type by using two important results due to Szekelyhidi.
