Iterated quasi-arithmetic mean-type mappings

Paweł Pasteczka. "Iterated quasi-arithmetic mean-type mappings." Colloquium Mathematicae 144.2 (2016): 215-228. <http://eudml.org/doc/286081>.

@article{PawełPasteczka2016,
abstract = {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.},
author = {Paweł Pasteczka},
journal = {Colloquium Mathematicae},
keywords = {gaussian product; invariant means; quasi-arithmetic means; iteration; mean; Mean-type mapping},
language = {eng},
number = {2},
pages = {215-228},
title = {Iterated quasi-arithmetic mean-type mappings},
url = {http://eudml.org/doc/286081},
volume = {144},
year = {2016},
}

TY - JOUR
AU - Paweł Pasteczka
TI - Iterated quasi-arithmetic mean-type mappings
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 2
SP - 215
EP - 228
AB - 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.
LA - eng
KW - gaussian product; invariant means; quasi-arithmetic means; iteration; mean; Mean-type mapping
UR - http://eudml.org/doc/286081
ER -