Title

On Cauchy differences of all orders

Document Type

Article

Publication Date

8-1991

Department

Department of Mathematical Sciences

Abstract

This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differences f(x + y)-f(x)-f(y) for maps f between groups were characterized by Jessen, Karpf, and Thorup [8] through the use of first partial Cauchy differences. Our results are similar and extend their result to higher order differences. Our results also extend those of Heuvers [6] for mappings between vector spaces over the rationals.

Publisher's Statement

© 1991 Birkhäuser Verlag. Publisher’s version of record: https://doi.org/10.1007/BF01818486

Publication Title

Aequationes Mathematicae

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