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Volume 7, Issue 2, Article 53 |
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On a Generalized $n-$inner Product and the Corresponding Cauchy-Schwarz Inequality
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Authors: |
Kostadin Trencevski, Risto Malcevski, |
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Keywords:
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Cauchy-Schwarz inequality, $n$-inner product, $n$-norm. |
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Date Received:
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22/11/04 |
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Date Accepted:
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27/02/06 |
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Subject Codes: |
46C05, 26D20.
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Editors: |
Constantin P. Niculescu, |
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Abstract: |
In this paper is defined an  -inner product of type  where  ,  are vectors from a vector space  . This definition generalizes the definition of Misiak of -inner product [2], such that in special case if we consider only such pairs of sets  and  which differ for at most one vector, we obtain the definition of Misiak. The Cauchy-Schwarz inequality for this general type of -inner product is proved and some applications are given.
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