A convergence result on random products of mappings in metric trees

Saleh Abdullah Al-Mezel, Mohamed Amine Khamsi

Research output: Contribution to journalArticlepeer-review


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.

Original languageBritish English
Article number57
JournalFixed Point Theory and Applications
StatePublished - 2012


  • 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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