Jensen type quadratic-quadratic mapping in Banach spacesopen access
- Authors
- Park, Choonkil; Hong, Seong-Ki; Kim, Myoung-Jung
- Issue Date
- Nov-2006
- Publisher
- Korean Mathematical Society
- Keywords
- Cauchy Rassias stability; Functional equation; Quadratic mapping
- Citation
- Bulletin of the Korean Mathematical Society, v.43, no.4, pp.703 - 709
- Indexed
- SCOPUS
KCI
- Journal Title
- Bulletin of the Korean Mathematical Society
- Volume
- 43
- Number
- 4
- Start Page
- 703
- End Page
- 709
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/180760
- DOI
- 10.4134/BKMS.2006.43.4.703
- ISSN
- 1015-8634
- Abstract
- Let X, Y be vector spaces. It is shown that if an even mapping f : X → Y satisfies f(0) = 0 and f(x + y/2 + z) + f(x + y/2 - z) + f(x - y/2 + z) (0.1) + f(x - y/2 - z) = f(x) + f(y) + 4f(z) for all x, y, z ∈ X, then the mapping f : X → Y is quadratic. Furthermore, we prove the Cauchy-Rassias stability of the functional equation (0.1) in Banach spaces.
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