### Abstract

We study the following Minkowski-type inequality (*) S_{a0,b0}(x_{1} + y_{1},x_{2} + y_{2}) ≤ S_{a1,b1} (x_{1},x_{2}) + S_{a2,b2} (y_{1},y_{2}) (x_{1},x_{2},y_{1},y_{2} ∈ ℝ_{+}), where S_{a,b} is the two variable Gini mean defined by (Formula Presented) The case when a_{0} = a_{1} = a_{2} and b_{0} = b_{1} = b_{2} was investigated by LOSONCZI-PÁLES [LP96]. Generalizing their result, we give necessary and sufficient conditions (concerning the parameters a_{i},b_{i}, ∈ ℝ) for the inequality above to hold. As a consequence of this result, it turns out that any inequality of the form (*) is weakening of an analogous inequality where all the participating means are equal to each other.

Original language | English |
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Pages (from-to) | 203-216 |

Number of pages | 14 |

Journal | Publicationes Mathematicae |

Volume | 57 |

Issue number | 1-2 |

Publication status | Published - Dec 1 2000 |

### Keywords

- Gini means
- Minkowski inequality
- Two variable homogeneous means

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Publicationes Mathematicae*,

*57*(1-2), 203-216.