### Abstract

In this paper, we completely describe those Cauchy-differences that can also be written as a quasisum, i.e., we solve the functional equation f(x) + f(y) - f(x + y) = a(b(x) + b(y)) under strict monotonicity assumptions on the unknown functions a, b. As an application of the result obtained, we solve a functional equation arising in utility theory. Cauchy-difference, quasisum.

Original language | English |
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Pages (from-to) | 381-398 |

Number of pages | 18 |

Journal | Publicationes Mathematicae |

Volume | 65 |

Issue number | 3-4 |

Publication status | Published - Dec 1 2004 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Járai, A., Maksa, G., & Páles, Z. (2004). On Cauchy-differences that are also quasisums.

*Publicationes Mathematicae*,*65*(3-4), 381-398.