On a generalized n-inner product and the corresponding Cauchy-Schwarz inequality
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915125447884800 |
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| author | Trenčevski, Kostadin Malčeski, Risto |
| author_facet | Trenčevski, Kostadin Malčeski, Risto |
| contents | In this paper is defined an $n$-inner product of type $\langle {\bf a}_1,\cdots ,{\bf a}_n\vert {\bf b}_1\cdots {\bf b}_n\rangle $ where ${\bf a}_1,\cdots ,{\bf a}_n$, ${\bf b}_1, \cdots ,{\bf b}_n$ are vectors from a vector space $V$. This definition generalizes the definition of Misiak of $n$-inner product \cite{2}, such that in special case if we consider only such pairs of sets $\{ {\bf a}_1,\cdots ,{\bf a}_1\}$ and $\{ {\bf b}_1\cdots {\bf b}_n\}$ which differ for at most one vector, we obtain the definition of Misiak. The Cauchy-Schwarz inequality for this general type of $n$-inner product is proved and some applications are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a generalized n-inner product and the corresponding Cauchy-Schwarz inequality Trenčevski, Kostadin Malčeski, Risto General Mathematics 46C05, 26D20 In this paper is defined an $n$-inner product of type $\langle {\bf a}_1,\cdots ,{\bf a}_n\vert {\bf b}_1\cdots {\bf b}_n\rangle $ where ${\bf a}_1,\cdots ,{\bf a}_n$, ${\bf b}_1, \cdots ,{\bf b}_n$ are vectors from a vector space $V$. This definition generalizes the definition of Misiak of $n$-inner product \cite{2}, such that in special case if we consider only such pairs of sets $\{ {\bf a}_1,\cdots ,{\bf a}_1\}$ and $\{ {\bf b}_1\cdots {\bf b}_n\}$ which differ for at most one vector, we obtain the definition of Misiak. The Cauchy-Schwarz inequality for this general type of $n$-inner product is proved and some applications are given. |
| title | On a generalized n-inner product and the corresponding Cauchy-Schwarz inequality |
| topic | General Mathematics 46C05, 26D20 |
| url | https://arxiv.org/abs/2501.16340 |