Generalized Hyers-Ulam stability for general additive functional equations on non-Archimedean random Lie \(C^\ast\)-algebras. (English) Zbl 1499.39127
Summary: In this paper, using the fixed point method, we prove some results related to the generalized Hyers-Ulam stability of homomorphisms and derivations in non-Archimedean random \(C^\ast\)-algebras and non-Archimedean random Lie \(C^\ast\)-algebras for the generalized additive functional equation
\[
\sum_{1 \leq i < j \leq n} f\left(\frac{x_i+x_j}{2} + \sum^{n-2}_{l=1,k_l\neq i,j} x_{k_l}\right) = \frac{(n-1)^2}{2} \sum^n_{i=1} f(x_i)
\]
where \(n \in \mathbb{N}\) is a fixed integer with \(n \geq 3\).
MSC:
| 39B82 | Stability, separation, extension, and related topics for functional equations |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 46S10 | Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis |
| 46L57 | Derivations, dissipations and positive semigroups in \(C^*\)-algebras |
Keywords:
derivation in \(C^\ast\)-algebras; derivation in Lie \(C^\ast\)-algebras; fixed point method; a general additive functional equation; generalized Hyers-Ulam stability; homomorphism in \(C^\ast\)-algebras; homomorphism in Lie \(C^\ast\)-algebras; non-Archimedean random spaceReferences:
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