On the stability of an n-dimensional cubic functional equation

Let n⩾2n⩾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∗C∗-algebra, and the stability using the alternative fixed point of an n-dimensional cubic functional equation in Banach spaces:f(∑j=1n−1xj+2xn)+f(∑j=1n−1xj−2xn)+∑j=1n−1f(2xj)=2f(∑j=1n−1xj)+4∑j=1n−1(f(xj+xn)+f(xj−xn)).