A fixed point approach to the stability of an AQ-functional equation on b-Banach modules

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the following mixed additive and quadratic functional equation f(kx + y) + f(kx-y) = f(x + y) + f(x-y) + (k-1) [(k + 2) f(x) + kf(-x)] (ke ℕ, k ≠ 1) in β-Banach modules on a Banach algebra. © 2012 Xu and Rassias; licensee Springer.