Approximation of a generalized additive mapping in multi-Banach modules and isomorphisms in multi-C*-algebras: a fixed-point approach

Abstract

Let , be vector spaces. It is shown that if an odd mapping satisfies the functional equation(rf(Sigma(d)(j=1)x(j)/r) + Sigma(r(j)=0,1 Sigma j=1d iota(j)=1)) rf(Sigma(d)(j=1)(-1)(iota(j))x(j)/r)= (C-d-1(j)-(d-1) Cj-1 + 1) Sigma(d)(j=1) f(x(j))then the odd mapping is additive, and we use a fixed-point method to prove the Hyers-Ulam stability of the functional equation (0.1) in multi-Banach modules over a unital multi--algebra. As an application, we show that every almost linear bijection of a unital multi--algebra onto a unital multi--algebra is a -algebra isomorphism when for all unitaries , all , and .MSC: 39B52, 46L05, 47H10, 47B48.