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HYERS-ULAM-RASSIAS STABILITY OF HOMOMORPHISMS IN QUASI-BANACH ALGEBRAS
- Authors
- Park, Chun-Gil
- Issue Date
- Dec-2006
- Publisher
- Banach Mathematical Research Group
- Keywords
- Hyers-Ulam-Rassias stability; functional equation; homomorphism in quasi-Banach algebra; p-Banach algebra; generalized derivation
- Citation
- Banach Journal of Mathematical Analysis, v.1, no.1, pp 23 - 32
- Pages
- 10
- Indexed
- SCIE
SCOPUS
- Journal Title
- Banach Journal of Mathematical Analysis
- Volume
- 1
- Number
- 1
- Start Page
- 23
- End Page
- 32
- ISSN
- 2662-2033
1735-8787
- 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: Sigma(n)(i=1) f(Sigma(n)(j=1) q(x(i) - x(j)) + nf(Sigma(n)(j=1) qxi) = nq( (Sigma(n)(j=1) f(x(i)) 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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