Parametrized means and limit properties of their Gaussian iterations
作者:
Highlights:
•
摘要
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.
论文关键词:Mean,Parametrized mean,Gauss composition,Elliptic integrals,Invariance,Convergence of successive iterates
论文评审过程:Received 18 March 2014, Revised 5 March 2015, Accepted 19 March 2015, Available online 11 April 2015.
论文官网地址:https://doi.org/10.1016/j.amc.2015.03.085