On the stability of the orthogonal Pexiderized Cauchy equation

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers–Ulam stability of the orthogonal Cauchy functional equation of Pexider type f1(x+y)=f2(x)+f3(y), x⊥y in which ⊥ is the orthogonality in the sense of Rätz.