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The purpose of this paper is to solve the generalized Hyers–Ulam stability problem for a k –additive functional equation Dm,if (x, y) = 0, on the basis of direct method, where k=4m+i is a positive integer for each i = −1, 0, 1 and 2. Mathematics subject classification (2000): 39B82, 39B52.

On the Hyers-Ulam-Rassias stability problem for approximately k-additive mappings and functional inequalities