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- W2564731819 abstract "Let S be a semigroup, H a 2-torsion free, abelian group and $$C^2f$$ the second order Cauchy difference of a function $$f:S rightarrow H$$ . 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 Frechet’s functional equation and to polynomials of degree less than or equal to 2." @default.
- W2564731819 created "2017-01-06" @default.
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- W2564731819 date "2016-12-19" @default.
- W2564731819 modified "2023-10-04" @default.
- W2564731819 title "The kernel of the second order Cauchy difference on semigroups" @default.
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- W2564731819 doi "https://doi.org/10.1007/s00010-016-0453-8" @default.
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