Stability of a Generalized Euler-Lagrange Type Additive Mapping and Homomorphisms in C-Algebras
نویسندگان
چکیده
Let X,Y be Banach modules over a C∗-algebra and let r1, . . . , rn ∈ R be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital C∗-algebra: ∑n j 1 f −rjxj ∑ 1≤i≤n,i / j rixi 2 ∑n i 1 rif xi nf ∑n i 1 rixi . We show that if ∑n i 1 ri / 0, ri, rj / 0 for some 1 ≤ i < j ≤ n and a mapping f : X → Y satisfies the functional equation mentioned above then the mapping f : X → Y is Cauchy additive. As an application, we investigate homomorphisms in unital C∗-algebras.
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