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Vahidi, Javad; Lee, Sung Jin

Stability of homomorphisms on fuzzy Lie \(C^*\)-algebras via fixed point method. (English) Zbl 1309.39021

J. Inequal. Appl. 2014, Paper No. 33, 8 p. (2014).
Summary: In this paper, first, we define fuzzy \(C^*\)-algebras and fuzzy Lie \(C^*\)-algebras; then, using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in fuzzy \(C^*\)-algebras and fuzzy Lie \(C^*\)-algebras for an \(m\)-variable additive functional equation.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
46S40 Fuzzy functional analysis
39B52 Functional equations for functions with more general domains and/or ranges
46L05 General theory of \(C^*\)-algebras

Keywords:

fuzzy normed spaces; additive functional equation; fixed point method; homomorphism in \(C^*\)-algebras; homomorphism in Lie \(C^*\)-algebras; generalized Hyers-Ulam stability
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References:

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