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

  • Authors:

  • Szabolcs Baják;Zsolt Páles

  • Affiliations:

  • Institute of Mathematics, University of Debrecen, 4010 Debrecen, Pf 12, Hungary;Institute of Mathematics, University of Debrecen, 4010 Debrecen, Pf 12, Hungary

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

Our aim is to solve the so-called invariance equation in the class of two-variable Gini means {G"p","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 G"p","q(G"a","b(x,y),G"c","d(x,y))=G"p","q(x,y)(x,y@?R"+) be valid. We recall that, for pq, the Gini mean G"p","q is defined by G"p","q(x,y):=(x^p+y^px^q+y^q)^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.