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

Szabolcs Baják, Z. Páles

Research output: Article

13 Citations (Scopus)

Abstract

We solve the so-called invariance equation in the class of two-variable Stolarsky means {S p q: p, q ε R}, i.e., we find necessary and sufficient conditions on the six parameters a,b,c,d,p,q such that the identity S p,q(S a,b(x,y),S c,d(x,y)) = S p q(x,y) (x,y ε R +), be valid. We recall that, for pq(p - q) ≠ 0 and x ≠y, the Stolarsky mean S p,qis defined by S p q(x, y):=(q(x p/p(x q 1/pq In the proof first we approximate the Stolarsky mean and we use the computer-algebra system Maple V Release 9 to compute the Taylor expansion of the approximation up to 12th order, which enables us to describe all the cases of the equality.

Original languageEnglish
Pages (from-to)3219-3227
Number of pages9
JournalApplied Mathematics and Computation
Volume216
Issue number11
DOIs
Publication statusPublished - aug. 1 2010

Fingerprint

Stolarsky Means
Invariance
Algebra
Computer algebra system
Maple
Taylor Expansion
Equality
Valid
Necessary Conditions
Sufficient Conditions
Approximation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

Computer aided solution of the invariance equation for two-variable Stolarsky means. / Baják, Szabolcs; Páles, Z.

In: Applied Mathematics and Computation, Vol. 216, No. 11, 01.08.2010, p. 3219-3227.

Research output: Article

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