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The kernel of the second order Cauchy difference on semigroups
Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review
Dokumenter
- The kernel of the second order Cauchy difference on semigroups
Accepteret manuskript, 982 KB, PDF-dokument
DOI
- https://doi.org/10.1007/s00010-016-0453-8
Forlagets udgivne version
Let S be a semigroup, H a 2-torsion free, abelian group and C 2f the second order Cauchy difference of a function f: S→ H. Assuming that H is uniquely 2-divisible or S is generated by its squares we prove that the solutions f of C 2f= 0 are the functions of the form f(x) = j(x) + B(x, x) , where j is a solution of the symmetrized additive Cauchy equation and B is bi-additive. Under certain conditions we prove that the terms j and B are continuous, if f is. We relate the solutions f of C 2f= 0 to Fréchet’s functional equation and to polynomials of degree less than or equal to 2.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Aequationes Mathematicae |
| Vol/bind | 91 |
| Nummer | 2 |
| Sider (fra-til) | 279–288 |
| Antal sider | 10 |
| ISSN | 0001-9054 |
| DOI | |
| Status | Udgivet - 2017 |
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