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INNER PRODUCT SPACES AND FUNCTIONAL EQUATIONS
- Issue Date
- Feb-2011
- Publisher
- Kluwer Academic Publishers
- Keywords
- additive mapping; quadratic mapping; functional equation associated with inner product space; generalized Hyers-Ulam stability
- Citation
- Journal of Computational Analysis and Applications, v.13, no.2, pp 296 - 304
- Pages
- 9
- Indexed
- SCIE
SCOPUS
- Journal Title
- Journal of Computational Analysis and Applications
- Volume
- 13
- Number
- 2
- Start Page
- 296
- End Page
- 304
- ISSN
- 1521-1398
1572-9206
- Abstract
- In [7], Th.M. Rassias introduced the following equality Sigma(n)(i,j=1) parallel to x(i) - x(j)parallel to(2) = 2n Sigma(n)(i=1) parallel to x(i)parallel to(2), Sigma(n)(i=1) x(i)=0 for a fixed integer n >= 3. Let V IV be real vector spaces. In this paper, we show that, if a mapping f : V -> W satisfies Sigma(n)(i,j=1) f(x(i) - x(j)) = 2n Sigma(n)(i=1) f(x(i)) for all x(1), ... , x(n) is an element of V with Sigma(n)(i=1) x(i)=0, then the mapping f: V -> W is realized as the sum of an additive mapping and a quadratic mapping. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.1) in real Banach spaces.
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