On monotone nonexpansive mappings in L1([0,1])

Mohamed Amine Khamsi, Abdul Rahim Khan

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13 Scopus citations


Let the set C⊂L1([0,1]) be nonempty, convex and compact for the convergence almost everywhere and T:C→C be a monotone nonexpansive mapping. In this paper, we study the behavior of the Krasnoselskii-Ishikawa iteration sequence {fn} defined by fn+1=λfn+(1−λ)T(fn), n=1,2,…, λ∈(0,1). Then we prove a fixed point theorem for these mappings. Our result is new and was never investigated.

Original languageBritish English
Article number94
JournalFixed Point Theory and Applications
Issue number1
StatePublished - 26 Dec 2015


  • convergence almost everywhere
  • fixed point
  • Ishikawa iteration
  • Krasnoselskii iteration
  • Lebesgue measure
  • monotone mapping
  • nonexpansive mapping


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