Approximately additive Schwartz distributions
type: Item
instance of: scholarly article
title: Approximately additive Schwartz distributions
zbMATH Open document ID: 1104.39022
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: A distributional analogue of the Rassias inequality \(\| f(x+y)-f(x)-f(y)\| \leq \varepsilon(\| x\| ^p+\| y\| ^p)\) was investigated for \(p=4, 6, 8, \dots\) by \textit{J. Chung} in [J. Math. Anal. Appl. 300, No. 2, 343--350 (2004; Zbl 1066.39028)]. In this paper, the author generalizes his previous stability result to all \(p \geq 0, p \neq 1\), and in fact for a certain general control function \(\psi(x, y)\) instead of \(\varepsilon(\| x\| ^p+\| y\| ^p)\), in the space of Schwartz (tempered) distributions.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 46F10
zbMATH DE Number: 5073037
zbMATH Keywords: Cauchy functional equation
zbMATH Keywords: stability
zbMATH Keywords: heat kernel
zbMATH Keywords: Gauss transform
zbMATH Keywords: Rassias inequality
zbMATH Keywords: Schwartz (tempered) distributions
author: Jaeyoung Chung
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.01.010
OpenAlex ID: W1966642600
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DOI: 10.1016/J.JMAA.2006.01.010
description: scientific article; zbMATH DE number 5073037