## Stability of homomorphisms and generalized derivations on Banach algebras.(English)Zbl 1187.39046

Summary: We prove the generalized Hyers-Ulam stability of homomorphisms and generalized derivations associated to the following functional equation $$f(2x+y)+f(x+2y)=f(3x)+f(3y)$$ on Banach algebras.

### 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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