Parametrized means and limit properties of their Gaussian iterations

Justyna Jarczyk

Applied Mathematics and Computation, 2015, vol. 261, issue C, 81-89

Abstract: We propose the notion of a mean depending on a parameter, define Gauss-type iterates of parametrized mean-type mapping and study their limit behaviour. Also a suitable invariance property of the limit function is established. In such a way we obtain an extension of generalized Gaussian algorithm (Theorem 2.5) to the case of a compact set of parameters. In particular, we generalize some well known results of J. Matkowski dealing with iterates of mean-type mappings not depending on parameter.

Keywords: Mean; Parametrized mean; Gauss composition; Elliptic integrals; Invariance; Convergence of successive iterates (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:261:y:2015:i:c:p:81-89

DOI: 10.1016/j.amc.2015.03.085

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