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 inActa mathematica Hungarica Vol. 150; no. 1; pp. 131 - 141
Main Authors Bahyrycz, A., Páles, Zs, Piszczek, M.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2016
Springer Nature B.V
Subjects
Errors
Functional equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Stability
metric group
functional equation
asymptotic stability
stability
39B82
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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:0236-5294
1588-2632
DOI:10.1007/s10474-016-0629-7