Iterated quasi-arithmetic mean-type mappings

• Autorzy: Paweł Pasteczka
• Języki publikacji: 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.

Kategorie tematyczne

• 26B15: Integration: length, area, volume
• 26A18: Iteration
• 39B12: Iteration theory, iterative and composite equations
• 26E60: Means

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 2
• Strony: 215-228

Daty

wydano

2016

Twórcy

autor

Paweł Pasteczka

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

Identyfikatory

DOI

10.4064/cm6479-2-2016