### Abstract

Given two continuous functions f, g : I → R such that g is positive and f / g is strictly monotone, and a probability measure μ on the Borel subsets of [0, 1], the two variable mean M_{f, g ; μ} : I^{2} → I is defined byM_{f, g ; μ} (x, y) : = (frac(f, g))^{-1} (frac(∫_{0}^{1} f (t x + (1 - t) y) d μ (t), ∫_{0}^{1} g (t x + (1 - t) y) d μ (t))) (x, y ∈ I) . The aim of this paper is to study the comparison problem of these means, i.e., to find conditions for the generating functions (f, g) and (h, k) and for the measures μ, ν such that the comparison inequalityM_{f, g ; μ} (x, y) ≤ M_{h, k ; ν} (x, y) (x, y ∈ I) holds.

Original language | English |
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Pages (from-to) | 135-146 |

Number of pages | 12 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 345 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 1 2008 |

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### Keywords

- Comparison problem
- Generalized Gini means
- Generalized integral means

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*345*(1), 135-146. https://doi.org/10.1016/j.jmaa.2008.04.004

**Comparison of means generated by two functions and a measure.** / Losonczi, László; Páles, Z.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 345, no. 1, pp. 135-146. https://doi.org/10.1016/j.jmaa.2008.04.004

}

TY - JOUR

T1 - Comparison of means generated by two functions and a measure

AU - Losonczi, László

AU - Páles, Z.

PY - 2008/9/1

Y1 - 2008/9/1

N2 - Given two continuous functions f, g : I → R such that g is positive and f / g is strictly monotone, and a probability measure μ on the Borel subsets of [0, 1], the two variable mean Mf, g ; μ : I2 → I is defined byMf, g ; μ (x, y) : = (frac(f, g))-1 (frac(∫01 f (t x + (1 - t) y) d μ (t), ∫01 g (t x + (1 - t) y) d μ (t))) (x, y ∈ I) . The aim of this paper is to study the comparison problem of these means, i.e., to find conditions for the generating functions (f, g) and (h, k) and for the measures μ, ν such that the comparison inequalityMf, g ; μ (x, y) ≤ Mh, k ; ν (x, y) (x, y ∈ I) holds.

AB - Given two continuous functions f, g : I → R such that g is positive and f / g is strictly monotone, and a probability measure μ on the Borel subsets of [0, 1], the two variable mean Mf, g ; μ : I2 → I is defined byMf, g ; μ (x, y) : = (frac(f, g))-1 (frac(∫01 f (t x + (1 - t) y) d μ (t), ∫01 g (t x + (1 - t) y) d μ (t))) (x, y ∈ I) . The aim of this paper is to study the comparison problem of these means, i.e., to find conditions for the generating functions (f, g) and (h, k) and for the measures μ, ν such that the comparison inequalityMf, g ; μ (x, y) ≤ Mh, k ; ν (x, y) (x, y ∈ I) holds.

KW - Comparison problem

KW - Generalized Gini means

KW - Generalized integral means

UR - http://www.scopus.com/inward/record.url?scp=44149103818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44149103818&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2008.04.004

DO - 10.1016/j.jmaa.2008.04.004

M3 - Article

VL - 345

SP - 135

EP - 146

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -