Approximation of a generalized additive mapping in multi-Banach modules and isomorphisms in multi-C*-algebras: a fixed-point approachopen access
- Authors
- Park, Choonkil; Saadati, Reza
- Issue Date
- Sep-2012
- Publisher
- SPRINGER INTERNATIONAL PUBLISHING AG
- Keywords
- C*-algebra isomorphism; fixed point; generalized additive functional equation; generalized Hyers-Ulam stability; multi-Banach module over multi-[InlineEquation not available: see fulltext.]-algebra
- Citation
- ADVANCES IN DIFFERENCE EQUATIONS, pp.1 - 14
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN DIFFERENCE EQUATIONS
- Start Page
- 1
- End Page
- 14
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/164754
- DOI
- 10.1186/1687-1847-2012-162
- ISSN
- 1687-1839
- Abstract
- Let , be vector spaces. It is shown that if an odd mapping satisfies the functional equation (rf(Sigma(d)(j=1)x(j)/r) + Sigma(r(j)=0,1 Sigma j=1d iota(j)=1)) rf(Sigma(d)(j=1)(-1)(iota(j))x(j)/r) = (C-d-1(j)-(d-1) Cj-1 + 1) Sigma(d)(j=1) f(x(j)) then the odd mapping is additive, and we use a fixed-point method to prove the Hyers-Ulam stability of the functional equation (0.1) in multi-Banach modules over a unital multi--algebra. As an application, we show that every almost linear bijection of a unital multi--algebra onto a unital multi--algebra is a -algebra isomorphism when for all unitaries , all , and . MSC: 39B52, 46L05, 47H10, 47B48.
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