A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation
type: Item
instance of: scholarly article
title: A generalization of the Hyers-Ulam-Rassias stability of the Pexider equation
zbMATH Open document ID: 0957.39008
author: Yang-Hi Lee
author: Kil-Woung Jun
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-03-29T00:00:00Z
review text: Let \(V\) be a normed vector space and \(X\) a Banach space, and let \(f,g,h: V\to X\). The authors prove that the Pexider equation \[ f(x+y)= g(x)+h(y) \] is stable in the following sense: If there exists a real number \(p\neq 1\), such that \[ \bigl\|f(x+y)- g(x)-h(y) \bigr\|\leq\|x \|^p+ \|y\|^p \] for all \(x,y\in V\setminus \{0\}\), then there exists exactly one additive map \(T:V\to X\) such that \[ \bigl\|f(x)- T(x)-f(0) \bigr\|\leq C(p)\|x\|^p \] for all \(x\in V\). Here \(C(p)\) is a certain specified constant.
reviewed by: Henrik Stetkær
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1496314
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: Banach space
zbMATH Keywords: Pexider equation
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6832
OpenAlex ID: W2016495160
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DOI: 10.1006/JMAA.2000.6832
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description: scientific article; zbMATH DE number 1496314