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Stability of the Jensen-type functional equation in \(C^{\ast}\)-algebras: a fixed point approach. (English) Zbl 1167.39020

Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in \(C^{\ast }\)-algebras and Lie \(C^{\ast }\)-algebras and also of derivations on \(C^{\ast }\)-algebras and Lie \(C^{\ast }\)-algebras for the Jensen-type functional equation \(f((x+y)/2)+f((x - y)/2)=f(x)\).

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46L57 Derivations, dissipations and positive semigroups in \(C^*\)-algebras
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References:

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