The Pexiderized Apollonius-Jensen type additive mapping and isomorphisms between C*-algebras

Abstract

Let X, Y be Banach modules over a C*-algebra. We prove the Hyers-Ulam-Rassias stability of the following Pexiderized functional equation in Banach modules over a unital C*-algebra: [GRAPHICS] It is shown that mappings F,G,H:XY satisfy the functional Equation (0.1) and F(0)=G(0) if and only if the mappings F,G,H:XY are Cauchy additive and F=G=H. As an application, we show that bijective mappings F,G,H:AB of a unital C*-algebra A onto a unital C*-algebra B are C*-algebra isomorphisms when F(0)=G(0)=0, F is [image omitted]-linear and H(2duy)=F(2du)G(y) for all unitaries uA all yA and all