Stability of a mixed functional equation in several variables on Banach modules

In this paper, we establish the general solution of the functional equation ∑i=1nf(xi−1n∑j=1nxj)=∑i=1nf(xi)−nf(1n∑i=1nxi)(n≥2), and use a fixed point method to prove its generalized Hyers–Ulam stability in Banach modules over a unital Banach algebra.