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

C. E. Chidume, Naseer Shahzad, Habtu Zegeye

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

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
Volume25
Issue number3-4
DOIs
Publication statusPublished - May 1 2004

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Completely Continuous
Banach spaces
Convergence Theorem
Kadec-Klee Property
Converge
Uniformly Convex Banach Space
Retract
Retraction
Hilbert spaces
Proximity
Hilbert space
Banach space
Analogue
Closed
Operator

All Science Journal Classification (ASJC) codes

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

Cite this

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Convergence theorems for mappings which are asymptotically nonexpansive in the intermediate sense. / Chidume, C. E.; Shahzad, Naseer; Zegeye, Habtu.

In: Numerical Functional Analysis and Optimization, Vol. 25, No. 3-4, 01.05.2004, p. 239-257.

Research output: Contribution to journalArticle

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