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In this paper, we define random Lie $$C^*$$ C ∗ -algebras, then we apply a fixed point theorem to investigate some new stability results for $$(\alpha ,\beta ,\gamma )$$ ( α , β , γ ) -derivations on random Lie $$C^*$$ C ∗ -algebras associated with a generalized Cauchy–Jensen type additive functional equation.
In this paper, we prove the generalized Hyers–Ulam stability of the following mixed additive–quadratic functional equation: 2f(x+y2)+f(x−y2)+f(y−x2)=f(x)+f(y) in various spaces.
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