Iterated quasi-arithmetic mean-type mappings

Paweł Pasteczka

Colloquium Mathematicae, Tome 144 (2016), p. 215-228 / Harvested from The Polish Digital Mathematics Library

Résumé

We work with a fixed N-tuple of quasi-arithmetic means $M₁,...,M_{N}$ generated by an N-tuple of continuous monotone functions $f₁,...,f_{N}: I → ℝ$ (I an interval) satisfying certain regularity conditions. It is known [initially Gauss, later Gustin, Borwein, Toader, Lehmer, Schoenberg, Foster, Philips et al.] that the iterations of the mapping $I^{N} ∋ b ↦ (M₁(b),...,M_{N}(b))$ tend pointwise to a mapping having values on the diagonal of $I^{N}$. Each of [all equal] coordinates of the limit is a new mean, called the Gaussian product of the means $M₁,..., M_{N}$ taken on b. We effectively measure the speed of convergence to that Gaussian product by producing an effective-doubly exponential with fractional base-majorization of the error.

Détail

Publié le : 2016-01-01

Zbl 06575001

EUDML-ID : urn:eudml:doc:286081