Orthogonal stability of the generalized quadratic functional equations in the sense of Rätz

Let (X, ⊥) be an orthogonality module in the sense of Rätz over a unital Banach algebra A and Y be a real Banach module over A. In this paper, we apply the alternative fixed point theorem for proving the Hyers-Ulam stability of the orthogonally generalized k-quadratic functional equation of the form