Stability of homomorphisms on fuzzy Lie \(C^*\)-algebras via fixed point method. (English) Zbl 1309.39021
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 stabilityReferences:
[1] | doi:10.1090/S0002-9904-1968-11933-0 · Zbl 0157.29904 · doi:10.1090/S0002-9904-1968-11933-0 |
[2] | doi:10.1016/j.jmaa.2008.03.039 · Zbl 1228.39025 · doi:10.1016/j.jmaa.2008.03.039 |
[3] | doi:10.1007/BF02936069 · Zbl 1077.46060 · doi:10.1007/BF02936069 |
[4] | doi:10.1016/j.camwa.2010.08.055 · Zbl 1205.39023 · doi:10.1016/j.camwa.2010.08.055 |
[5] | doi:10.1016/j.fss.2007.07.011 · Zbl 1179.46060 · doi:10.1016/j.fss.2007.07.011 |
[6] | doi:10.1016/j.ins.2008.05.032 · Zbl 1160.46336 · doi:10.1016/j.ins.2008.05.032 |
[7] | doi:10.1016/j.aml.2011.05.033 · Zbl 1236.39031 · doi:10.1016/j.aml.2011.05.033 |
[8] | doi:10.1016/j.jmaa.2003.10.051 · Zbl 1051.46052 · doi:10.1016/j.jmaa.2003.10.051 |
[9] | doi:10.1007/s00574-005-0029-z · Zbl 1091.39007 · doi:10.1007/s00574-005-0029-z |
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