### Abstract

All strictly monotonie solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.

Original language | English |
---|---|

Pages (from-to) | 989-998 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 4 |

Publication status | Published - 2001 |

### Fingerprint

### Keywords

- Binary gamble
- Convexity
- Functional equation
- Rank-dependent expected utility

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*129*(4), 989-998.

**A functional equation arising from ranked additive and separable utility.** / Aczél, János; Maksa, Gyula; Ng, Che Tat; Páles, Z.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 129, no. 4, pp. 989-998.

}

TY - JOUR

T1 - A functional equation arising from ranked additive and separable utility

AU - Aczél, János

AU - Maksa, Gyula

AU - Ng, Che Tat

AU - Páles, Z.

PY - 2001

Y1 - 2001

N2 - All strictly monotonie solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.

AB - All strictly monotonie solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.

KW - Binary gamble

KW - Convexity

KW - Functional equation

KW - Rank-dependent expected utility

UR - http://www.scopus.com/inward/record.url?scp=33646852086&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646852086&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33646852086

VL - 129

SP - 989

EP - 998

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -