Some remarks on the stability of the Cauchy equation and completeness
type: Item
instance of: scholarly article
title: Some remarks on the stability of the Cauchy equation and completeness
zbMATH Open document ID: 1482.39040
author: Harald Fripertinger
author: Jens Schwaiger
published in: Aequationes Mathematicae
publication date: 2021-12-06T00:00:00Z
review text: Let \(S\) be a commutative semigroup and \(X\) be a Banach space. It is well known that every function \(f:S\to X\) such that the norm of its Cauchy difference is bounded by a constant is close to some additive function. In this paper, the authors discuss the case when the bound is a suitable non-constant function. They also find some characterizations of completeness by stability in Archimedean and non-Archimedean spaces.
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 7439037
zbMATH Keywords: Cauchy equation
zbMATH Keywords: Hyers-Ulam stability
zbMATH Keywords: completeness
MaRDI profile type: Publication
full work available at URL: s00010-021-00804-y
OpenAlex ID: W3162779845
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DOI: 10.1007/S00010-021-00804-Y
description: scientific article; zbMATH DE number 7439037