Quadratic mappings associated with inner product spaces
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 박춘길 | - |
dc.date.accessioned | 2021-08-03T23:22:55Z | - |
dc.date.available | 2021-08-03T23:22:55Z | - |
dc.date.created | 2021-06-30 | - |
dc.date.issued | 2008-08-22 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/64079 | - |
dc.description.abstract | In \cite{ra84}, Th.M. Rassias proved that the norm defined over a real vector space $V$ is induced by an inner product if and only if for a fixed integer $n \ge 2$ \begin{eqnarray*} \sum_{i=1}^n \left\|x_i - \frac{1}{n} \sum_{j=1}^n x_j\right\|^2 = \sum_{i=1}^n\|x_i\|^2 - n \left\|\frac{1}{n}\sum_{i=1}^n x_i\right\|^2 \end{eqnarray*} holds for all $x_1, \cdots, x_n \in V$. Let $V, W$ be real vector spaces. It is shown that if an even mapping $f : V \rightarrow W$ satisfies \begin{eqnarray} \sum_{i=1}^{2n} f\left(x_i - \frac{1}{2n} \sum_{j=1}^{2n} x_j\right) = \sum_{i=1}^{2n}f(x_i) - 2n f\left(\frac{1}{2n}\sum_{i=1}^{2n} x_i\right) \end{eqnarray} for all $x_1, \cdots, x_{2n} \in V$, then the even mapping $f : V \rightarrow W$ is quadratic. Furthermore, we prove the generalized Hyers-Ulam stability of the quadratic functional equation {\rm (0.1)} in Banach spaces. | - |
dc.publisher | 파키스탄수학회 | - |
dc.title | Quadratic mappings associated with inner product spaces | - |
dc.type | Conference | - |
dc.contributor.affiliatedAuthor | 박춘길 | - |
dc.identifier.bibliographicCitation | International Pure Mathematics Conference | - |
dc.relation.isPartOf | International Pure Mathematics Conference | - |
dc.citation.title | International Pure Mathematics Conference | - |
dc.citation.conferencePlace | Quaid-i-Azam University | - |
dc.type.rims | CONF | - |
dc.description.journalClass | 1 | - |
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