Abstract
AbstractExplicit forms of invariant means for all mean-type mappings generated by the bivariable classical arithmetic, geometric and harmonic means (complementary to the Gauss $$\mathcal {AGM}$$
AGM
-theorem) are given. A generalization for higher dimension mean-type mappings as well as two open problems and an application in determining implicit solutions of some functional equations, are presented.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,General Mathematics
Reference12 articles.
1. Aczél, J.: Lectures on Functional Equations and Their Applications. Academic Press, New York and London (1966)
2. Borwein, J.M., Borwein, P.B.: Pi and the AGM, Monographies et Études de la Société Mathématique du Canada. Wiley, Toronto (1987)
3. Bullen, P.S.: Handbook of Means and Their Inequalities. Kluwer, Dordrecht/ Boston/London (2003)
4. Daróczy, Z., Páles, Zs.: Gauss-composition of means and the solution of the Matkowski–Sutô problem. Publ. Math. Debrecen 61(1–2), 157–218 (2002)
5. Gray, J.J.: A commentary on Gauss’s mathematical diary, 1796–1814. Expo. Math. 2, 97–130 (1982)