A convergence result on random products of mappings in metric trees - Al-Mezel, Saleh Abdullah; Khamsi, Mohamed Amine (Fixed point theory and algorithms for sciences and engineering, 2012)
Let X be a metric space and { T 1 , ..., 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 x 0 ∈ D ; and x n + 1 = T r ( n ) ( x n ) , for all n ≥ 0 . 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.