Abstract
Let $q$ be a positive rational number and $n$ be a nonnegative integer. We prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras and of generalized derivations on quasi-Banach algebras for the following functional equation: \begin{eqnarray*} \sum_{i=1}^{n} f \left( \sum_{j=1}^{n}q (x_i-x_j) \right) + n f \left(\sum_{i=1}^{n} q x_i \right) = nq \sum_{i=1}^{n} f(x_i) . \end{eqnarray*} This is applied to investigate isomorphisms between quasi-Banach algebras.~The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.
Citation
Chun-Gil Park. "Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras." Banach J. Math. Anal. 1 (1) 23 - 32, 2007. https://doi.org/10.15352/bjma/1240321552
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