Aequationes mathematicae

, Volume 87, Issue 1, pp 147–157

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

Open Access
Article

DOI: 10.1007/s00010-013-0193-y

Cite this article as:
Chmieliński, J. Aequat. Math. (2014) 87: 147. doi:10.1007/s00010-013-0193-y
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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.

Mathematics Subject Classification (2010)

39B82 46B03 46B20 46C15 

Keywords

Normed space equivalent to inner product space approximate parallelogram law von Neumann–Jordan constant quadratic functional equation stability of functional equations 
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© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Instytut MatematykiUniwersytet Pedagogiczny w KrakowieKrakówPoland

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