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• # Artykuł - szczegóły

## Colloquium Mathematicum

2016 | 144 | 2 | 215-228

## Iterated quasi-arithmetic mean-type mappings

EN

### Abstrakty

EN
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.

215-228

wydano
2016

### Twórcy

autor
• Institute of Mathematics, Pedagogical University of Cracow, Podchorążych 2, 30-084 Kraków, Poland