### 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 - 2004 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

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

**On Cauchy-differences that are also quasisums.** / Járai, Antal; Maksa, Gyula; Páles, Zsolt.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 65, no. 3-4, pp. 381-398.

}

TY - JOUR

T1 - On Cauchy-differences that are also quasisums

AU - Járai, Antal

AU - Maksa, Gyula

AU - Páles, Zsolt

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=11144352723&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11144352723&partnerID=8YFLogxK

M3 - Article

VL - 65

SP - 381

EP - 398

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -