Communications in Mathematical Analysis

A Characterization of Inner Product Spaces Concerning an Euler-Lagrange Identity

Abstract

In this paper we present a new criterion on characterization of real inner product spaces concerning the Euler-Lagrange type identity

$$\|r_2x_1-r_1x_2\|^2 + \|r_1x_1+r_2x_2\|^2=(r_1^2+r_2^2)(\|x_1\|^2+\|x_2\|^2)\,.$$

Article information

Source
Commun. Math. Anal., Volume 8, Number 2 (2010), 16-21.

Dates
First available in Project Euclid: 21 April 2010

https://projecteuclid.org/euclid.cma/1271890667

Mathematical Reviews number (MathSciNet)
MR2569953

Zentralblatt MATH identifier
1194.46037

Citation

Moslehian, Mohammad S.; Rassias, John M. A Characterization of Inner Product Spaces Concerning an Euler-Lagrange Identity. Commun. Math. Anal. 8 (2010), no. 2, 16--21. https://projecteuclid.org/euclid.cma/1271890667

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