Banach Journal of Mathematical Analysis

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras

Chun-Gil Park

Full-text: Open access

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.

Article information

Source
Banach J. Math. Anal., Volume 1, Number 1 (2007), 23-32.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240321552

Digital Object Identifier
doi:10.15352/bjma/1240321552

Mathematical Reviews number (MathSciNet)
MR2350191

Zentralblatt MATH identifier
1135.39017

Subjects
Primary: 39B52: Equations for functions with more general domains and/or ranges
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 47Jxx: Equations and inequalities involving nonlinear operators [See also 46Txx] {For global and geometric aspects, see 58-XX}

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

Citation

Park, Chun-Gil. Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras. Banach J. Math. Anal. 1 (2007), no. 1, 23--32. doi:10.15352/bjma/1240321552. https://projecteuclid.org/euclid.bjma/1240321552


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