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

Let be a normed space. If 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.

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Bibliographic Details
Published in:Aequationes mathematicae Vol. 87; no. 1-2; pp. 147 - 157
Main Author: Chmieliski, Jacek
Format: Journal Article
Language:English
Published: Basel Springer Basel 01.03.2014
Springer Nature B.V
Subjects:
Analysis
Approximation
Combinatorics
Equivalence
Law
Linear equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Parallelograms
Quadratic programming
Stability
Texts
Theorems
quadratic functional equation
46C15
von Neumann–Jordan constant
46B03
approximate parallelogram law
stability of functional equations
46B20
Normed space equivalent to inner product space
39B82
ISSN:0001-9054, 1420-8903
Online Access:Get full text
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Description
Summary:Let be a normed space. If 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.
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ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-013-0193-y