A convergence result on random products of mappings in metric trees

Abstract

Let X be a metric space and {T ^sub 1^, ..., T ^sub N^} be a finite family of mappings defined on D X. Let r : [arrow right] {1,..., N} be a map that assumes every value infinitely often. The purpose of this article is to establish the convergence of the sequence (x ^sub N^) defined by

[Equation not available: see fulltext.]

In particular we prove Amemiya and Ando's theorem in metric trees without compactness assumption. This is the first attempt done in metric spaces. These type of methods have been used in areas like computerized tomography and signal processing.

Mathematics Subject Classification 2000: Primary: 06F30; 46B20; 47E10.[PUBLICATION ABSTRACT]