General quadratic-additive type functional equation and its stability (Q1751435)

Summary: We investigate the general functional equation of the form \begin{multline*} f(a x + b y + c z) - a b f(x + y) - b c f(y + z)) - (a c f(x + z) - a((a + 1) / 2\\ - b - c) f(x) - b((b + 1) / 2 - a - c) f(y) - c((c + 1) / 2 - a - b) f(z) -(a(a - 1) / 2) f(- x)\\ - (b(b - 1) / 2) f(- y) -(c(c - 1) / 2) f(- z) = 0, \end{multline*} whose solutions are quadratic-additive mappings in connection with stability problems.