Approximate fixed point sequences and convergence theorems for asymptotically pseudocontractive mappings

C. E. Chidume, Hab Zegeye

Research output: Contribution to journalReview article

10 Citations (Scopus)

Abstract

Let K be a nonempty closed convex and bounded subset of a real Banach space E and T : K → K be uniformly L-Lipschitzian, uniformly asymptotically regular with sequence {εn}, and asymptotically pseudocontractive with constant {kn}, where {kn} and {εn} satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by xn+1 := (1 - λn)xn + λnTnxn - λnθn(xn - x1), for all integers n ≥ 1, where {λn} and {θn} are real sequences satisfying appropriate conditions, then ∥xn - Txn∥ → 0 as n → ∞. Moreover, if E is reflexive, and has uniform normal structure with coefficient N(E) and L < N(E)1/2 and has a uniformly Gâteaux differentiable norm, and T satisfies an additional mild condition, then {xn} also converges strongly to a fixed point of T.

Original languageEnglish
Pages (from-to)354-366
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume278
Issue number2
DOIs
Publication statusPublished - Feb 15 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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