Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
471109 | Computers & Mathematics with Applications | 2009 | 7 Pages |
Abstract
Our aim is to solve the so-called invariance equation in the class of two-variable Gini means {Gp,q:p,q∈R}{Gp,q:p,q∈R}, i.e., to find necessary and sufficient conditions on the 6 parameters a,b,c,d,p,qa,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≠qp≠q, the Gini mean Gp,qGp,q is defined by Gp,q(x,y):=(xp+ypxq+yq)1p−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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Szabolcs Baják, Zsolt Páles,