Superstability of the Cauchy, Jensen and isometry equations
type: Item
instance of: scholarly article
title: Superstability of the Cauchy, Jensen and isometry equations
zbMATH Open document ID: 0929.39015
DOI: 10.1007/BF03322824
author: Jacek Tabor
published in: Results in Mathematics
publication date: 2000-01-25T00:00:00Z
review text: The author generalizes the results of \textit{J. Tabor} [Result Math. 32, No. 1-2, 145-158 (1997; Zbl 0890.39024)] for the superstability of the Cauchy and Jensen functional equation almost everywhere. A theorem is also proved concerning the superstability of the isometry equation in inner product spaces. This implies a new characterization of the property: The isometry equation is superstable in the integral norm. The reader is referred to the book of \textit{D. H. Hyers}, \textit{G. Isac} and \textit{Th. M. Rassias} [Stability of functional equations in several variables (1998; Zbl 0907.39025)] for several results and a large list of references concerning stability of functional equations.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 1320610
zbMATH Keywords: superstability
zbMATH Keywords: isometry equations
zbMATH Keywords: Cauchy equation
zbMATH Keywords: group
zbMATH Keywords: Banach space
zbMATH Keywords: Jensen functional equation
Wikidata QID: Q112226183
reviewed by: Themistocles M. Rassias
MaRDI profile type: Publication
cites work: Note on almost additive functions
cites work: On the Stability of the Linear Functional Equation
cites work: Q3218572
cites work: On nonlinear perturbations of isometries
cites work: Lipschitz stability of the Cauchy and Jensen equations
cites work: Stability of the Cauchy type equations in the class of differentiable functions
cites work: Stability of the Cauchy type equations in \({\mathfrak L}_ p\) norms
cites work: Q3259049
full work available at URL: https://doi.org/10.1007/bf03322824
OpenAlex ID: W2050819652
description: scientific article; zbMATH DE number 1320610