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2007 Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras
Chun-Gil Park
Banach J. Math. Anal. 1(1): 23-32 (2007). DOI: 10.15352/bjma/1240321552


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.


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Chun-Gil Park. "Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras." Banach J. Math. Anal. 1 (1) 23 - 32, 2007.


Published: 2007
First available in Project Euclid: 21 April 2009

zbMATH: 1135.39017
MathSciNet: MR2350191
Digital Object Identifier: 10.15352/bjma/1240321552

Primary: 39B52‎
Secondary: 46B03 , 47Jxx

Keywords: functional equation , generalized derivation , homomorphism in quasi-Banach algebra , Hyers-Ulam-Rassias stability , p-Banach algebra

Rights: Copyright © 2007 Tusi Mathematical Research Group

Vol.1 • No. 1 • 2007
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