Comparison of means generated by two functions and a measure

László Losonczi, Z. Páles

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)135-146
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume345
Issue number1
DOIs
Publication statusPublished - Sep 1 2008

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Set theory
Probability Measure
Generating Function
Monotone
Continuous Function
Strictly
Subset

Keywords

  • Comparison problem
  • Generalized Gini means
  • Generalized integral means

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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

In: Journal of Mathematical Analysis and Applications, Vol. 345, No. 1, 01.09.2008, p. 135-146.

Research output: Contribution to journalArticle

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