Inner product spaces and quadratic functional equations
- Authors
- Park, C.; Park, W.-G.; Rassias, T.M.
- Issue Date
- 2016
- Publisher
- Springer New York LLC
- Keywords
- Hyers-Ulam stability; Inner product space; Quadratic functional equation; Quadratic mapping
- Citation
- Springer Proceedings in Mathematics and Statistics, v.155, pp.137 - 151
- Indexed
- SCOPUS
- Journal Title
- Springer Proceedings in Mathematics and Statistics
- Volume
- 155
- Start Page
- 137
- End Page
- 151
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/155537
- DOI
- 10.1007/978-3-319-28443-9_10
- ISSN
- 2194-1009
- Abstract
- In this paper, we prove that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer n ≥ 2 (Formula presented) holds for all x1, …,xn ∈ V. Let V, W be real vector spaces. It is shown that if a mapping f: V → W satisfies (Formula presented) or (Formula presented) for all x1, …, xn ∈ V, then the mapping f: V → W is Cauchy additive-quadratic. Furthermore, we prove the Hyers-Ulam stability of the above quadratic functional equations in Banach spaces.
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