On the stability of a quadratic Jensen type functional equation
type: Item
instance of: scholarly article
title: On the stability of a quadratic Jensen type functional equation
zbMATH Open document ID: 1007.39026
DOI: 10.1016/S0022-247X(02)00093-8
author: Young Whan Lee
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-09-08T00:00:00Z
review text: For real linear spaces \(X\) and \(Y\), \(f: X\to Y\) satisfies the functional equation \[ 9f\Biggl({x+ y+ z\over 3}\Biggr)+ f(x)+ f(y)+ f(z)= 4\Biggl[f\Biggl({x+ y\over 2}\Biggr)+ f\Biggl({y+ z\over 2}\Biggr)+ f\Biggl({z+ x\over 2}\Biggr)\Biggr] \] if and only if \(f(x)= Q(x)+ A(x)+ B\) for an additive function \(A: X\to Y\), a quadratic function \(Q: X\to Y\), and an element \(B\in Y\). (\(Q\) quadratic means that \(Q(x+ y)+ Q(x- y)= 2Q(x)+ 2Q(y)\) for all \(x,y\in X\).) Hyers-Ulam-Rassias stability of this so-called quadratic Jensen type functional equation is also established.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1797527
zbMATH Keywords: linear spaces
zbMATH Keywords: functional equation
zbMATH Keywords: Hyers-Ulam-Rassias stability
zbMATH Keywords: quadratic Jensen type functional equation
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00093-8
OpenAlex ID: W2087652676
description: scientific article; zbMATH DE number 1797527