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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
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