Generalized Hyers-Ulam stability for general additive functional equations in quasi-\(\beta \)-normed spaces
type: Item
instance of: scholarly article
title: Generalized Hyers-Ulam stability for general additive functional equations in quasi-\(\beta \)-normed spaces
zbMATH Open document ID: 1168.39015
author: Hark-Mahn Kim
author: J. M. Rassias
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-06-10T00:00:00Z
review text: The authors investigate the generalized Hyers-Ulam stability problem for the following functional equation \[ \displaystyle\sum_{1\leq i \leq j\leq n}g\left(\frac{x_i+x_j}{2}+\displaystyle\sum_{l=1,k_l\neq i,j}^{n-2}x_{k_l}\right) =\frac{(n-1)^2}{2}\displaystyle\sum_{i=1}^{n}g(x_i), \] where \(n \geq 3\), \(g:X\to Y\) is a mapping and \(X\), \(Y\) are normed spaces. They also investigate this problem, when \(X\) is a quasi-\(\beta\) normed space.
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5563870
zbMATH Keywords: generalized Hyers-Ulam stability
zbMATH Keywords: quasi-\(\beta\) normed spaces
zbMATH Keywords: (\(\beta.p)\)-Banach spaces
zbMATH Keywords: contractively subadditive
zbMATH Keywords: expansively superadditive
zbMATH Keywords: functional equation
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.03.005
OpenAlex ID: W2016808667
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DOI: 10.1016/J.JMAA.2009.03.005
description: scientific article; zbMATH DE number 5563870