Functional equations related to inner product spaces
type: Item
instance of: scholarly article
title: Functional equations related to inner product spaces
zbMATH Open document ID: 1177.39041
DOI: 10.1155/2009/907121
author: Choonkil Park
author: Won-Gil Park
author: A. Najati
published in: Abstract and Applied Analysis
publication date: 2009-11-10T00:00:00Z
full work available at URL: https://eudml.org/doc/45667
review text: Summary: Let \(V,W\) be real vector spaces. It is shown that an odd mapping \(f:V\to W\) satisfies \[ \sum^{2n}_{i=1}f(x_i-1/2n\sum_{j=1}^{2n}x_j)=\sum_{i=1}^{2n}f(x_i)-2_nf(1/2n\sum_{i=1}^{2n}x_i) \] for all \(x_1,\dots,x_{2n}\in V\) if and only if the odd mapping \(f:V\to W\) is Cauchy additive. Furthermore, we prove the generalized Hyers-Ulam stability of the above functional equation in real Banach spaces.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5627618
zbMATH Keywords: inner product spaces
zbMATH Keywords: Cauchy additive
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: functional equation
zbMATH Keywords: Banach spaces
MaRDI profile type: Publication
Wikidata QID: Q58646692
OpenAlex ID: W2159347530
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description: scientific article; zbMATH DE number 5627618