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Generalized Hyers-Ulam stability of an Euler-Lagrange type additive mapping.
- Source :
- Journal of Difference Equations & Applications; Dec2006, Vol. 12 Issue 12, p1277-1288, 12p
- Publication Year :
- 2006
-
Abstract
- Let X, Y be Banach modules over a [image omitted] -algebra and let [image omitted] be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital [image omitted] -algebra:[image omitted] We show that if [image omitted] and an odd mapping [image omitted] satisfies the functional equation (0.1) then the odd mapping [image omitted] is Cauchy additive. As an application, we show that every almost linear bijection [image omitted] of a unital [image omitted] -algebra A onto a unital [image omitted] -algebra B is a [image omitted] -algebra isomorphism when [image omitted] for all unitaries [image omitted] , all [image omitted] , and all [image omitted] . The concept of generalized Hyers-Ulam stability originated from 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 12
- Issue :
- 12
- Database :
- Complementary Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 24905655
- Full Text :
- https://doi.org/10.1080/10236190600986925