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 |
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Dordrecht
Springer Netherlands
01.10.2016
Springer Nature B.V |
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| Abstract | 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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| AbstractList | 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. |
| Author | Páles, Zs Piszczek, M. Bahyrycz, A. |
| Author_xml | – sequence: 1 givenname: A. surname: Bahyrycz fullname: Bahyrycz, A. organization: Department of Mathematics, Pedagogical University of Cracow, Faculty of Applied Mathematics, AGH University of Science and Technology – sequence: 2 givenname: Zs surname: Páles fullname: Páles, Zs email: pales@science.unideb.hu organization: Institute of Mathematics, University of Debrecen – sequence: 3 givenname: M. surname: Piszczek fullname: Piszczek, M. organization: Department of Mathematics, Pedagogical University of Cracow |
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| Cites_doi | 10.1090/S0002-9904-1951-09511-7 10.1090/S0002-9939-1978-0507327-1 10.1007/s10474-013-0347-3 10.2969/jmsj/00210064 10.1016/j.na.2011.06.052 10.1007/s000100050109 10.1007/BF01831117 10.1017/S1446181100008051 10.1007/BF03322226 10.1073/pnas.27.4.222 10.1090/S0002-9939-98-04680-2 10.1007/s00010-007-2892-8 10.1016/j.jmaa.2004.03.011 10.1007/s000100050058 10.1007/978-1-4612-1790-9 10.4064/ap-58-2-147-159 10.1073/pnas.95.22.12772 10.1142/4875 10.4064/ap-72-3-207-217 10.1007/978-3-662-38380-3 10.5486/PMD.1987.34.1-2.15 |
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| Copyright | Akadémiai Kiadó, Budapest, Hungary 2016 Copyright Springer Science & Business Media 2016 |
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| References_xml | – ident: CR22 – volume: 24 start-page: 77 year: 2013 end-page: 108 ident: CR26 article-title: An instructive treatment and some natural extensions of a set-valued function of Páles publication-title: Math. Pannon. contributor: fullname: Száz – ident: CR14 – ident: CR16 – volume: 58 start-page: 147 year: 1993 end-page: 159 ident: CR2 article-title: On some generalized invariant means and their application to the stability of the Hyers–Ulam type publication-title: Ann. Polon. Math. contributor: fullname: Badora – ident: CR10 – volume: 57 start-page: 223 year: 1951 end-page: 237 ident: CR7 article-title: Classes of transformations and bordering transformations publication-title: Bull. Amer. Math. Soc. doi: 10.1090/S0002-9904-1951-09511-7 contributor: fullname: Bourgin – ident: CR6 – volume: 72 start-page: 297 year: 1978 end-page: 300 ident: CR24 article-title: On the stability of the linear mapping in Banach spaces publication-title: Proc. Amer. Math. 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| Title | Asymptotic stability of the Cauchy and Jensen functional equations |
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