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

✍ Scribed by Szabolcs Baják; Zsolt Páles

Book ID
104008555
Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
444 KB
Volume
58
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

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

be valid. We recall that, for p = q, the Gini mean G p,q is defined by G p,q (x, y) :=

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.

📜 SIMILAR VOLUMES

On the continuation of solutions for ell
On the continuation of solutions for elliptic equations in two variables
✍ Frank Müller 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 210 KB

We consider nonlinear elliptic differential equations of second order in two variables F (x, y, z(x, y), z x (x, y), . . . , z yy (x, y)) = 0, (x, y) ∈ ⊂ R 2 . Supposing analyticity of F , we prove analyticity of the real solution z = z(x, y) in the open set . Furthermore, we show that z may be cont