A convergence result on random products of mappings in metric spaces

Mohamed Amine Khamsi, Issam Louhichi

Research output: Contribution to journalArticlepeer-review

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)(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.

Original languageBritish English
Article number43
JournalFixed Point Theory and Applications
Volume2012
DOIs
StatePublished - 2012

Keywords

  • Computerized tomography
  • Convex feasibility problem
  • Convex programming
  • Fejér monotone sequence
  • Image reconstruction
  • Image recovery
  • Innate bounded regularity
  • Kaczmarz's method
  • Nonexpansive mapping
  • Projection algorithm
  • Projective mapping
  • Random product
  • Signal processing
  • Unrestricted iteration
  • Unrestricted product

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