Summary
This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differencesf(x + y)−f(x)−f(y) for mapsf 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.
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