Cauchy-Rassias stability of linear mappings in Banach modules associated with a generalized Jensen type mapping
The authors prove the stability of the generalized Jensen type functional equation \[ f\big(x_1+\sum_{j=2}^{2n}(-1)^jx_j\big)-f\big(x_1+\sum_{j=2}^{2n}(-1)^{j-1}x_j\big)=2\sum_{j=2}^{2n}(-1)^jf(x_j) \] in Banach modules over a unital \(C^*\)-algebra. They also prove the stability of homomorphisms in Poisson Banach modules over a unital Poisson \(C^*\)-algebra and investigate homomorphisms between \(C^*\)-algebras and Poisson \(JC^*\)-algebras.
Poisson Banach module over Poisson \(C^*\)-algebra
generalized Jensen type functional equation
scientific article; zbMATH DE number 5716976