Title

Convergence Result on Random Products of Mappings in Metric Trees

Authors

Saleh A. Al-Mezel, King Abdulaziz University
Mohamed A. Khamsi, University of Texas at El PasoFollow

Publication Date

3-1-2012

Document Type

Article

Comments

Al-Mezel, S.A. & Khamsi, M.A. Fixed Point Theory Appl (2012) 2012: 57. https://doi.org/10.1186/1687-1812-2012-57

Abstract

Let X be a metric space and {T1, ..., T N } be a finite family of mappings defined on D ⊂ X. Let r: ℕ → {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 n ) defined by

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.