Iterated Quasi-Arithmetic Mean-Type Mappings

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.

13 pages

Cited by in corpus (2)

• On the quasi-arithmetic Gauss-type iteration
• On the $L^1$ and pointwise divergence of continuous functions