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 $f_1(x+y)=f_2(x)+f_3(y)$, $x\perp y$ in which $\perp$ is the orthogonality in the sense of Ratz. 
Mohammad Sal Moslehian