Iterated Quasi-Arithmetic Mean-Type Mappings

TL;DR

This paper analyzes the convergence speed of iterative quasi-arithmetic mean mappings and applies the results to approximate continuous invariant functions.

Contribution

It provides new bounds on convergence rates for quasi-arithmetic mean iterations and demonstrates their use in function approximation.

Findings

Established upper bounds for convergence speed.

Applied results to approximate invariant continuous functions.

Enhanced understanding of mean-type iterative processes.

Abstract

For a family of quasi-arithmetic means satisfying certain smoothness condition we majorize the speed of convergence of the iterative sequence of self-mappings having a mean on each entry, described in the definition of Gaussian product, to relevant mean-type mapping. We apply this result to approximate any continuous function which is invariant with respect to such a self-mappings.