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Stability of the Jensen type functional equation in Banach algebras: a fixed point approach. (English) Zbl 1524.39055

Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in Banach algebras and of derivations on Banach algebras for the following Jensen type functional equation: \[ f (\frac{x+y}{2}) + f (\frac{x-y}{2}) = f(x) \]

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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