Generalized Hyers-Ulam stability of an Euler-Lagrange type additive mapping
- Authors
- Park, Choonkil; Park, Jae Myoung
- Issue Date
- Dec-2006
- Publisher
- TAYLOR & FRANCIS LTD
- Keywords
- generalized Hyers-Ulam stability; Euler-Lagrange type additive mapping; isomorphism between C-*-algebras; Th.M. Rassias' stability
- Citation
- JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, v.12, no.12, pp.1277 - 1288
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
- Volume
- 12
- Number
- 12
- Start Page
- 1277
- End Page
- 1288
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/180741
- DOI
- 10.1080/10236190600986925
- ISSN
- 1023-6198
- Abstract
- Let X, Y be Banach modules over a C*-algebra and let r(1),..., r(n) is an element of (0, infinity) be given. We prove the generalized Hyers-Ulam stability of the following functional equation in Banach modules over a unital C*-algebra: [GRAPHICS] We show that if r(1) =... = r(n) = r and an odd mapping f : X -> Y satisfies the functional equation (0.1) then the odd mapping f : X -> Y is Cauchy additive. As an application, we show that every almost linear bijection h : A -> B of a unital C*-algebra A onto a unital C*-algebra B is a C*-algebra isomorphism when h((n r)(d)uy) = h((nr)(d)u)h(y) for all unitaries u is an element of A, all y is an element of A, and all d is an element of Z. 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.
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