Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps

C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F(T) := {x ε K : T x = x} ≠ Ø. An iterative sequence {xn} is constructed for which ∥xn - Txn∥ → 0 as n → ∞. If, in addition, AT is assumed to be bounded, this conclusion still holds without the requirement that F(T] ≠ Ø. Moreover, if, in addition, E has a uniformly Gâteaux differentiable norm and is such that every closed bounded convex subset of K has the fixed point property for nonexpansive self-mappings, then the sequence {xn} converges strongly to a fixed point of T, Our iteration method is of independent interest.

Original languageEnglish
Pages (from-to)831-840
Number of pages10
JournalProceedings of the American Mathematical Society
Volume132
Issue number3
Publication statusPublished - Mar 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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