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 f 1 (x + y) = f 2 (x) + f 3 (y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz.
