On the stability of an n-dimensional cubic functional equation

Let n 2 be an integer number. In this paper, we investigate the generalized Hyers–Ulam–Rassias stability in Banach spaces and also Banach modules over a Banach algebra and a C∗-algebra, and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces: f n−1 j=1 xj +2xn + f n−1 j=1 xj − 2xn + n−1 j=1 f (2xj ) = 2f n−1 j=1 xj + 4 n−1 j=1 f (xj +xn) +f (xj − xn) . © 2006 Elsevier Inc. All rights reserved