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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.

Stability of homomorphisms on fuzzy Lie C ∗ -algebras via fixed point method