Inner product spaces and minimal values of functionals

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• 作者：Chelidze ; G.
• 关键词：Inner product space ; Hilbert space ; Optimal location
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2004
• 期刊代码：76_0022247x
• 类别：mt
• 出版时间：October 1, 2004
• 卷：298
• 期：1
• 页码：106-113
• 文件大小：102 K

摘要

We consider a real function which depends on the distances between a variable point and the points of a finite subset A of a linear normed space X. We show that X is an inner product space if this function attains its local minimum on a barycenter of points of A with well-chosen weights. Our result generalizes classical results about characterization of inner product spaces and answers a question of R. Durier, which was posed in his article [J. Math. Anal. Appl. 207 (1997) 220–239].