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

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

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

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Abstract

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

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