Hyers-Ulam-Rassias stability of n-apollonius type additive mapping and isomorphisms in c*-algebras

Abstract

In this paper, we prove Hyers-Ulam-Rassias stability of the following functional equation in Banach modules over a unital C*-algebra:which n is fixed integer and n ≤ 2. As an application, we show that every almost linear bijection h: A → B of a unital C*-algebra A onto a unital C*- algebra B is a C*-algebra isomorphism when for all unitaries u ∈ A, all y ∈ A, and all d ∈ Z.