TY - JOUR

T1 - A convergence result on random products of mappings in metric trees

AU - Al-Mezel, Saleh Abdullah

AU - Khamsi, Mohamed Amine

N1 - Funding Information:
The authors gratefully acknowledge the financial support provided by the University of Tabuk through the project of international cooperation with the University of Texas at El Paso. The authors thank the referee for pointing out some oversights and calling attention to some related literature.

PY - 2012

Y1 - 2012

N2 - Let X be a metric space and {T1,⋯, TN} 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 (xn) defined by x0 ∈ D; and xn+1 = Tr(n)(xn), 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.

AB - Let X be a metric space and {T1,⋯, TN} 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 (xn) defined by x0 ∈ D; and xn+1 = Tr(n)(xn), 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.

KW - Computerized tomography

KW - Convex feasibility problem

KW - Convex programming

KW - Metric tree

KW - Nonexpansive mapping

KW - Projection algorithm

KW - Projective mapping

KW - Random product

KW - Signal processing

KW - Unrestricted iteration

KW - Unrestricted product

UR - http://www.scopus.com/inward/record.url?scp=84873816090&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2012-57

DO - 10.1186/1687-1812-2012-57

M3 - Article

AN - SCOPUS:84873816090

SN - 1687-1820

VL - 2012

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

M1 - 57

ER -