摘要：We reformulate the following mixed type quadratic and additive functional equation with n-independent variables 2 f ∑ i = 1 n x i + ∑ 1 ≤ i , j ≤ n i ≠ j f ( x i - x j ) = ( n + 1 ) ∑ i = 1 n f ( x i ) + ( n - 1 ) ∑ i = 1 n f ( - x i ) as the equation for the spaces of generalized functions. Using the fundamental solution of the heat equation, we solve the general solution and prove the Hyers-Ulam stability of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Mathematics Subject Classification 2000: 39B82; 39B52.
