Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of...

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Bibliographic Details
Published in:arXiv.org 2016-01
Main Authors: Bahyrycz, Anna, Páles, Zsolt, Piszczek, Magdalena
Format: Article
Language:English
Subjects:
Asymptotic properties
Errors
Functional equations
Mathematical analysis
Stability
Online Access:Get full text
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Summary:The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations.
ISSN:2331-8422
DOI:10.48550/arxiv.1602.00300