### Abstract

The aim of this paper is to solve the comparison and equality problems of L-conjugate means of n ≥ 2 variables defined by (Equation presented) where L : 1^{n} → 1 is a symmetric mean on the open real interval 1 and φ → ℝ is continuous strictly monotonie function. The homogeneous L-conjugate means are also described. In the last section, the arithmetic mean is characterized as being the only mean that is conjugate arithmetic and quasiarithmetic.

Original language | English |
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Pages (from-to) | 331-341 |

Number of pages | 11 |

Journal | Mathematical Inequalities and Applications |

Volume | 4 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jul 2001 |

### Keywords

- Conjugate arithmetic means
- Convexity
- L-conjugate means
- Power means
- Quasiarithmetic means

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Daróczy, Z., & Páles, Z. (2001). On a class of means of several variables.

*Mathematical Inequalities and Applications*,*4*(3), 331-341. https://doi.org/10.7153/mia-04-32