Computer aided solution of the invariance equation for two-variable Gini means

Szabolcs Baják, Zsolt Páles

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Our aim is to solve the so-called invariance equation in the class of two-variable Gini means {Gp, q : p, q ∈ R}, i.e., to find necessary and sufficient conditions on the 6 parameters a, b, c, d, p, q such that the identity Gp, q (Ga, b (x, y), Gc, d (x, y)) = Gp, q (x, y) (x, y ∈ R+) be valid. We recall that, for p ≠ q, the Gini mean Gp, q is defined by Gp, q (x, y) : = (frac(xp + yp, xq + yq))frac(1, p - q) (x, y ∈ R+) . The proof uses the computer algebra system Maple V Release 9 to compute a Taylor expansion up to 12th order, which enables us to describe all the cases of the equality.

Original languageEnglish
Pages (from-to)334-340
Number of pages7
JournalComputers and Mathematics with Applications
Volume58
Issue number2
DOIs
Publication statusPublished - Jul 1 2009

Keywords

  • Computer algebra
  • Gauss composition
  • Gini means
  • Homogeneous means
  • Invariance equation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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