Approximation of linear mappings in Banach modules over C*-algebras

作者：Park Choonkil; Cho Yeol Je^*; Saadati Reza

来源：Journal of Inequalities and Applications, 2013, 2013(1): 185.

DOI：10.1186/1029-242X-2013-185

• fixed point
• Hyers-Ulam stability
• super-stability
• generalized Euler-Lagrange type additive mapping
• homomorphism
• C*-algebra

Let X, Y be Banach modules over a C*-algebra and let r(1), ..., r(n). R be given. Using fixed-point methods, we prove the stability of the following functional equation in Banach modules over a unital C*-algebra: %26lt;br%26gt;Sigma(n)(j=1) f(1/2 Sigma(1 %26lt;= i %26lt;= n,i not equal j) r(i)x(i) - 1/2r(j)x(j)) + Sigma(n)(i=1) r(i)f(x(i)) = nf(1/2 Sigma(n)(i=1) r(i)x(i)). %26lt;br%26gt;As an application, we investigate homomorphisms in unital C*-algebras.

• 出版日期2013