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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Published in | Acta mathematica Hungarica Vol. 150; no. 1; pp. 131 - 141 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Dordrecht
Springer Netherlands
01.10.2016
Springer Nature B.V |
Subjects | |
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. |
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ISSN: | 0236-5294 1588-2632 |
DOI: | 10.1007/s10474-016-0629-7 |