Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense

C. E. Chidume, Naseer Shahzad, Habtu Zegeye

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28 Citations (Scopus)


Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be a non-self mapping which is asymptotically nonexpansive in the intermediate sense with F(T) := {x ∈ K : Tx = x} ≠ Ø. A demiclosed principle for T is proved. Moreover, if T is completely continuous, an iterative sequence {xn} is constructed which converges strongly to some x* ∈ F(T). If T is not assumed to be completely continuous but the dual E* of E is assumed to have the Kadec-Klee property, then {xn} converges weakly to some x* ∈ F(T). The operator P which plays a central role in our proofs is, in this case, the Banach space analogue of the proximity map in Hilbert spaces.

Original languageEnglish
Pages (from-to)239-257
Number of pages19
JournalNumerical Functional Analysis and Optimization
Issue number3-4
Publication statusPublished - May 1 2004


All Science Journal Classification (ASJC) codes

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

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