## Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras.(English)Zbl 1135.39017

The Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras is proved for the following functional equation $\sum^{2}_{i=1} f\left(\sum^{2}_{j=1} q(x_{i}-x_{j})\right) +nf\left(\sum^{2}_{i=1} qx_{i}\right) =nq\sum^{2}_{i=1} f(x_{i}).$ This is applied to investigate isomorphisms between quasi-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 46B03 Isomorphic theory (including renorming) of Banach spaces 46H05 General theory of topological algebras

### Keywords:

generalized derivations; functional equation; isomorphisms
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