科研之友
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摘要
In this paper, we determine the general solution of the functional equation f(kx + y) + f (kx - y )= g(x + y) + g(x - y) + h(x) + (h) over bar (y) for fixed integers k with k not equal 0, +/- 1 without assuming any regularity condition on the unknown functions f,g,h,(h) over bar. The method used for solving these functional equations is elementary but exploits an important result due to Hosszu. The solution of this functional equation can also be determined in certain type of groups using two important results due to Szekelyhidi. The results improve and extend some recent results.
