A convergence result on random products of mappings in metric trees

Saleh Abdullah Al-Mezel; Mohamed Amine Khamsi

doi:10.1186/1687-1812-2012-57

A convergence result on random products of mappings in metric trees

Saleh Abdullah Al-Mezel, Mohamed Amine Khamsi

Mathematics

King Abdulaziz University

Research output: Contribution to journal › Article › peer-review

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 x₀ ∈ D; and xn+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.

Original language	British English
Article number	57
Journal	Fixed Point Theory and Applications
Volume	2012
DOIs	https://doi.org/10.1186/1687-1812-2012-57
State	Published - 2012

Keywords

Computerized tomography
Convex feasibility problem
Convex programming
Metric tree
Nonexpansive mapping
Projection algorithm
Projective mapping
Random product
Signal processing
Unrestricted iteration
Unrestricted product

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10.1186/1687-1812-2012-57

Cite this

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title = "A convergence result on random products of mappings in metric trees",

abstract = "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.",

keywords = "Computerized tomography, Convex feasibility problem, Convex programming, Metric tree, Nonexpansive mapping, Projection algorithm, Projective mapping, Random product, Signal processing, Unrestricted iteration, Unrestricted product",

author = "Al-Mezel, {Saleh Abdullah} and Khamsi, {Mohamed Amine}",

note = "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. ",

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doi = "10.1186/1687-1812-2012-57",

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journal = "Fixed Point Theory and Applications",

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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.

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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

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DO - 10.1186/1687-1812-2012-57

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SN - 1687-1820

VL - 2012

JO - Fixed Point Theory and Applications

JF - Fixed Point Theory and Applications

M1 - 57

ER -

A convergence result on random products of mappings in metric trees

Abstract

Keywords

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