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

Park, Chun-Gil

Banach J. Math. Anal. 1, No. 1, 23-32 (2007).

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.

Reviewer: Ioannis P. Stavroulakis (Ioannina)

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