### 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 |
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Pages (from-to) | 989-998 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2001 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Aczél, J., Maksa, G., Ng, C. T., & Páles, Z. (2001). A functional equation arising from ranked additive and separable utility.

*Proceedings of the American Mathematical Society*,*129*(4), 989-998. https://doi.org/10.1090/s0002-9939-00-05686-0