A general Minkowski-type inequality for two variable Gini means

Péter Czinder, Zsolt Páles

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We study the following Minkowski-type inequality (*) Sa0,b0(x1 + y1,x2 + y2) ≤ Sa1,b1 (x1,x2) + Sa2,b2 (y1,y2) (x1,x2,y1,y2 ∈ ℝ+), where Sa,b is the two variable Gini mean defined by (Formula Presented) The case when a0 = a1 = a2 and b0 = b1 = b2 was investigated by LOSONCZI-PÁLES [LP96]. Generalizing their result, we give necessary and sufficient conditions (concerning the parameters ai,bi, ∈ 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 languageEnglish
Pages (from-to)203-216
Number of pages14
JournalPublicationes Mathematicae
Volume57
Issue number1-2
Publication statusPublished - Dec 1 2000

Keywords

  • Gini means
  • Minkowski inequality
  • Two variable homogeneous means

ASJC Scopus subject areas

  • Mathematics(all)

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