TY - JOUR

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

AU - Khamsi, Mohamed Amine

AU - Louhichi, Issam

N1 - Funding Information:
The authors gratefully acknowledge the financial support from King Fahd University of Petroleum & Minerals for supporting research project SB 101021. The authors would also like to thank the referees for excellent suggestions and useful comments.

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)(x n), for all n ≥ 0. In particular, we extend the study of Bauschke [1] from the linear case of Hilbert spaces to metric spaces. Similarly we show that the examples of convergence hold in the absence of compactness. 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)(x n), for all n ≥ 0. In particular, we extend the study of Bauschke [1] from the linear case of Hilbert spaces to metric spaces. Similarly we show that the examples of convergence hold in the absence of compactness. 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 - Fejér monotone sequence

KW - Image reconstruction

KW - Image recovery

KW - Innate bounded regularity

KW - Kaczmarz's method

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=84873846891&partnerID=8YFLogxK

U2 - 10.1186/1687-1812-2012-43

DO - 10.1186/1687-1812-2012-43

M3 - Article

AN - SCOPUS:84873846891

SN - 1687-1820

VL - 2012

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

M1 - 43

ER -