On the Generalized Hyers-Ulam Stability of an Euler-Lagrange-Rassias Functional Equation

In this paper, the general solution and the generalized Hyers-Ulam-Rassias stability of the following Euler-Lagrange type quadratic functional equation f(x+ky)+f(y+kz)+f(z+kx)-kf(x+y+z) = (k²-k+1)(f(x)+f(y)+f(x)), for all k ∈ ℕ, is investigated.