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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 |

### Keywords:

fixed point methods; Hyers-Ulam stability; homomorphisms; \(C^{\ast }\)-algebras; Lie \(C^{\ast }\)-algebras; derivations; Jensen-type functional equation
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\textit{C. Park} and \textit{J. M. Rassias}, Abstr. Appl. Anal. 2009, Article ID 360432, 17 p. (2009; Zbl 1167.39020)

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