, Volume 87, Issue 1-2, pp 147-157,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 23 Mar 2013

Normed spaces equivalent to inner product spaces and stability of functional equations

Abstract

Let \({(X,\| \cdot \|)}\) be a normed space. If \({\| \cdot \|_i}\) is an equivalent norm coming from an inner product, then the original norm satisfies an approximate parallelogram law. Applying methods and results from the theory of stability of functional equations we study the reverse implication.